Pricing algorithms and computational price theory:
the building blocks of computational finance and IT business applications
Violetta Daniela Gómez Tagle Galindo
Master's Thesis
Faculty of Science and Forestry School of Computing
December 2017
i
UNIVERSITY OF EASTERN FINLAND, Faculty of Science and Forestry, Joensuu.
School of Computing – Computer Science
Student, Ing. Violetta Daniela Gómez Tagle Galindo: Pricing algorithms and computational price theory: the building blocks of computational finance and IT business applications.
Master’s Thesis, 147 pp., 69021 w.
Supervisor: Ph.D. Markku Tukiainen December, 2017
Abstract
Objective – the master thesis intends to discuss both the configuration and the context
of application of pricing algorithms, by providing a theoretical clarification of the concept and its contribution to the theory and practice of computational finance and information business systems.
Methodology/approach – the thesis entails 1) a conceptual analysis based on facts
and results documented in the literature, integrating all the acquired elements into a logical framework, 2) a formal derivation of the concepts of computational price theory and pricing algorithm, and 3) two-dimensional analysis of pricing algorithms (type of algorithms vs. type of financial problem it addresses or solves) of 8 pricing algorithms.
Findings – The thesis succeeds in developing a description of the architecture of
pricing algorithms on the basis of a computational price theory that is proposed, with a threefold distinction between pricing mechanism (or engine), allocation mechanism, and calibration procedure. A classification for pricing algorithms, a discussion of priceable assets, and a computational interpretation/derivation of key financial concepts are incorporated, which in its turn were positively related to purpose and scope of IT business applications. Analytically, the thesis finds informational and structural patterns underlying pricing algorithmic constructs. Contextually, the thesis finds that pricing algorithms constitute a family of algorithms on its own, with distinctive properties, features and relation with other algorithmic domains.
Research limitations/implications – The research scope of the thesis is limited to the
analysis of cases and studies documented in the literature, without explicit empirical verification based on actual market data.
Practical and theoretical implications – Due to the fact that the thesis is grounded in
economic, financial and computational theory, the scope of applicability of the thesis’
results widens. Implication for theory primarily reside in the clarification of the theoretical background supporting effective use of pricing algorithms. Practical implication is a contribution to the development of a working framework for pricing algorithms design and implementation, and to financial software engineering practice.
Originality/value – the thesis is, to the author’s knowledge, the first to analyze pricing
algorithms as an independent subject from a computational perspective. Furthermore, it analyzes aspects of algorithmic procedures, such as pricing algorithm taxonomy and architecture, which are only seldom studied by students of either computer science or finance/business management researchers.
Keywords: algorithms, pricing algorithms, asset pricing, computational price theory,
computational finance.
ACM Computing Classification (1998) Categories and Subject Descriptors: F2
CR Categories (ACM Computing Classification System, 1998 version):
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Disclaimer
When I explicitly label a concept or idea as “own work” means I didn’t directly use
any source to come to it, and also that I searched for it in the literature within my reach,
and didn’t found it.
iii
Foreword
"Whatever you are, be a good one." A. Lincoln said once. This thesis represents my personal commitment to honour that maxim. Written at the School of Computing, University of Eastern Finland, during the years 2014, 2015 and 2016, it has its own story behind the scenes. Allow me to briefly tell a little bit about it.
Although the focus area of research was very clear to me from the beginning, namely computational finance, narrowing the topic proved to be more than an easy challenge, because of the psychological pressure of finding meaningful specific areas of interest in order to come up with good research questions, the fact that a significant amount of literature relied on advanced mathematics for its full understanding or to explain the models therein proposed (a math level well above that required for my Master Programme), but basically because of the fact that the scattering of information regarding the topics thematically placed at the intersection of computer science and financial theory is mind-blowing: I literally felt like Cinderella collecting the beads from the room’s floor.
At first, the thesis topic was oriented toward investigating some the dynamics of computational networks in the financial arena, partly because I always have had the feeling that the way networking occurs in the financial environment is unique and therefore could be accounted as a potential source of explanation for financial transactions and events. However, I realized that more explanations about financial phenomena were not needed, being more important to try to fulfill what I identified as a vacuum in the description of a significant slice of computational techniques applied to finance in the form of pricing algorithms. So here it is.
In a personal domain, the preparation of this work overlapped with my gender reassignment MTF transitioning process, which although essentially is a personal matter, was impossible to completely dissociate from other facets of my life, specifically my academic work.
I want to extend my gratitude to my parents Rubén y Lupita (Q.E.P.D) which
supported me here in Finland in every way someone can be possibly supported, and
who I really intend to make proud. Unfortunately, my Mom passed away in late May
2017, and couldn’t witness my graduation. Be this work my personal tribute to her
beloved memory. Aunt Lulú who has been like a second Mom to me, my brother
Benjamin, Sylvia, old and new friends, as well as a lot of amazing people I have met
in this awesome country. I want to express a warm thankfulness to the School of
Computing of the UEF, to the UEF staff, and to my supervisor and the people who
dedicated part of their time to read my Thesis. Last but not least, to my teachers, who
I respect the most, and whose example I wish to live accordingly; after all, as Andy
Partridge once said: “You may leave school, but it never leaves you.”
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List of abbreviations
API Application Program Interface APK Asset Pricing Kernel
BI Business Intelligence
BM Brownin motion
EMH Efficient Market Hypothesis HFT High-Frequency Trading JVM Java Virtual Machine IoT Internet of Things
PDE Partial Differential Equation QoS Quality of Service
TM Turing Machine
DTM Deterministic TM NDTM Nondeterministic TM
UEF University of Eastern Finland
VaR Value-at-Risk
v
Conventions
Source referencing
[S]: This references provide an indirect support, the extension or modification is my responsibility only.
Measures: numbers are always expressed in long scale:
Million: 10
6= 1.000.000 Thousand million: 10
9= 1.000.000.000 Billion: 10
12= 1.000.000.000.000 Thousand billion: 10
15= 1.000.000.000.000.000 Trillion: 10
18= 1.000.000.000.000.000.000 Language: British English
Personal pronouns: throughout this work, when either a masculine or feminine personal pronoun
might be suitable, feminine pronouns (she, her) ae used.
vi
Contents
0 Formal requirements: research questions, methodological aspects, relevance
of the thesis topic, and organization of the document ... …. viii
0.1 Research questions ... viii
0.2 Methodology ... ix
0.3 Relevance of the thesis topic ... xi
0.4 Organization of the Master Thesis ... xiii
1 Introduction ... 1
1.1 Pricing topic preliminaries ... 2
Algorithms with a “financial personality”: fact or myth? ... 2
Putting pricing algorithms in context ... 4
General pricing mechanisms ... 5
Financial information patterns ... 5
1.2 Computational finance: a motivational entrée to a rugged landscape ... 6
Case study 1.1‒ Price manipulation in the Amazon Marketplace ...
7
Case study 1.2‒ The importance of financial management:the downfall of Nokia and the economic situation in Finland ...
10
Apendix 1.1‒ Different views of financial modelling as a framework for computational techniques ... 13
Apendix 1.2‒ Technology developments as a growth factor for financial markets 20 2 Financial and economic foundations for computational applications ... 25
2.1 Computational economies: private and differential information ... 25
2.2 Scarcity and computational complexity ... 28
2.3 Market efficiency and price implications of the efficient market hypothesis 29
2.4 Market efficiency: a computational approach ... 32
A computational view of market efficiency ... 32
A financial Turing test ... 32
Markets are efficient if and only if P = NP ... 32
2.5 A financial market’s building blocks ... 33
2.6 Financial modelling... 36
3 Algorithmics of financial markets... 39
3.1 The scope of computational finance ... 39
Computational finance taxonomy ... 40
Domain of algorithmic procedures in computational finance ... 40
3.2 Computability of financial markets operations ... 44
3.3 Computational modeling of financial operations ... 45
3.4 Algorithmic techniques used in computational finance ... 46
Case study 3.1‒ Grouping or agglomerating concepts for algorithms ...
48
3.5 Financial programming ... 50
Case study 3.2‒ Algorithmic hell: pricing synthetic CDOs ...
51
3.6 Architecture of financial applications ... 56
3.7 Right answers, wrong questions: artificial financial markets and virtual finan- cial operations ... 58
Apendix 3.1‒ Financial price anomalies ... 61
Apendix 3.2‒ Methodological aspects of computational finance applications... 63
Apendix 3.3‒ Financial time series clustering ... 74
vii
4 Computational price theory ... 82
4.1 Price theory: a financial and computational introduction ... 85
4.2 The "pricing problem" ... 85
4.3 Definition of computational price, pricing process and pricing algorithm ... 88
4.4 Priceable assets ... 91
Case study 4.1‒ Gold: a decoration accessory or a financial investment ...
92
4.5 Algorithmic pricing theoretical framework ... 93
Computational pricing theory ... 94
Derivation of a pricing algorithm ... 95
Fundamental Theorem of Asset Pricing ... 97
The Black-Scholes framework ... 97
Solving the Black-Scholes equation ... 98
4.6 Informational models for computational finance ... 99
4.7 Pricing algorithm characteristics: a coffee table discussion ... 101
Apendix 4.1‒ Priceable assets (complement) ... 103
5 Pricing algorithms ... 111
5.1 The scope of pricing algorithms ... 111
5.2 'Commercial pricing ... 115
5.3 Financial pricing I: Anatomy of a financial pricing algorithm ... 120
Approaches to models for pricing algorithms ... 120
Pricing mechanism internals ... 121
Schematization of the structure of a pricing algorithm ... 122
5.4 Financial pricing II: Review of pricing algorithms ... 123
Numerical methods ... 123
Analytical methods / Quasi-analytical methods ... 123
Problem vs. solution analysis of a sample of pricing algorithms... 124
6 Pricing on the run: pricing schemes for corporate governance ... 125
6.1 Corporate governance and price strategies ... 125
Discussion of results and conclusions ... 127
References ... 128
viii
Chapter 0. Formal requirements: research questions, methodological aspects, relevance of the thesis topic, and organization of the document.
A Master thesis in the area of computational finance at the UEF is a novelty. The topic itself only receives proper attention at specialized institutions. My intention in writing it (besides getting my Diploma) was to produce must be a substantial piece of academic work in a field that has not found enough coverage from theoretical computer science despite its socioeconomic relevance.
0.1 Research questions
A good formulation of research questions1 requires to determine if there is a potential problem regarding the interaction of finance and computational technologies which may be expressed as the need to produce a characterisation of pricing algorithms. So, in the sake of clarity and soundness, I structured the research questions according to the pursued research topic:
Research Topic Research questions Justification
1. Pricing algorithms (classification)
Is it viable to classify pricing algorithms as a family of algorithms, a fundamental algorithmic technique, or an algorithmic domain?2 If so, what would it be the general blueprint of a pricing algorithm?
Algorithmic classifications promote new ways of reasoning about given problems, enabling improved performance for computational procedures, and promoting better software engineering practices and orderliness in information management.
2. Pricing algorithms (characteristics &
properties)
What are the characteristics and properties of pricing algorithms?
How pricing algorithms are design and implemented?
Principles of design allow the inclusion of algorithms into engineering frameworks
3. Computational price theory
Is it necessary to develop a computational price theory to meet the model-building demands of computational finance applications?
Provide an essential foundation for computational pricing algorithms. A
suitable computational
interpretation of financial terms and concepts was found to be missing.
4. Impact of the automatization of pricing procedures
Does the analysis of the case studies presented in the literature suggests that computational algorithmic techniques are altering the dynamics of financial markets?
If so, what are the critical elements associated with the adoption of
The increasing criticality of software in the financial arena, and the size and complexity of financial applications, suggest that IT is not only automatizing financial markets’
operations, but actually expanding the markets artificially.
1 It is said that a good research question aims to address a topic or issue that of interesting for a community of people in the field of study, not just for the researcher or her research group only, while avoiding unnecessary complexities leading to unclear thoughts and therefore to a confused research process: it should be relevant and simple. Usually behind a good research question there is the tacit recognition of the existence of a problem to be solved, or at least the perception that there are unaccounted factors that limit the understanding of a certain process or event that has a practical impact and therefore worth to do the corresponding research. Finally, the scope shouldn’t be too broad or to narrow, the question must be researchable within the given time frame and location and manageable in terms of the researcher own academic abilities; and the information needed to provide an answer must be clearly identifiable, even if not always available. Source:
What Makes a Good Research Question?’ Writing Studio (http://twp.duke.edu/writing-studio).
February 6, 2014. Accessed online 15.04.2015.
2 Please refer to Appendix 5.1 Grouping concepts for algorithms, for terminology.
ix computational finance
techniques/applications?
5. Information management for computational finance applications
Which financial information features do software developers find desirable, and how well do informational frameworks and tools available meet these needs?
Informational properties of financial instruments and contracts and the way financial networks organize themselves around computational entities can provide new insight on how information is processed by highly automated financial markets?
Financial information management remains an open issue.
Identification of potential information sources as input for computational finance applications, as well innovative management methods for modelling financial information processes is indispensable. Since information reliability and entropy production in financial systems are stochastic in nature, a good information management and processing modules organization is key.
0.2 Methodology3
The Master thesis work comprised several stages:
Collecting data
Because the nature of thesis work is not empirical, there was no need to retrieve time series data from market monitoring sources. In every case some actual market data was used to support propositions, it comes from the literature reviewed; however, all data used was checked for consistency whenever possible.
Literature review
For most of the topics discussed here, the literature review comprised articles with a date span of approximately of 35 years, from 1982 to 2017. The vast majority of books, articles and other sources used are either open to the public, and available through the WWW, or to the students and staff of the UEF through the Nelly online portal of the UEF Library. The relevant criteria for the selection of articles were: (1) clearly state and support any proposition connected to the topics discussed in the thesis; (2) citations; and (3) published in prestigious journals or by well-recognized publishers.
Formulation of hypothesis and propositions
Once the research questions were established, the relevant working hypothesis were formulated accordingly to a short-term pilot research (not documented here):
H1: Pricing algorithms constitute a group of algorithms with distinctive characteristics and properties.
H2: It is uncertain if a computational price theory would be requirement for the development of financial software engineering, but the derivation of key financial concepts (such as ‘market’ or
‘risk’) in computational terms is indispensable for a proper understanding of pricing algorithms.
H3: Pricing algorithms in particular, as well as computational finance algorithms in general, have had a long range impact on the operational capabilities of the financial markets, the organization of information within them, and the way financial agents interact with each other.
3 Sources used throughout this section:
Berndtsson, Mikael; Hansson, Jörgen; Olsson, Björn and Lundell, Björn. Thesis Projects: A Guide for Students in Computer Science and Information Systems. Second edition, Springer, 2008. Chapter 2:
“Computer Science and Information Systems Research Projects”, pp. 9-14.
Rose, Susan; Spinks, Nigel and Canhoto, Ana Isabel. “Case study research design”, in Management Research: Applying the Principles. 2015.
Zucker, Donna M., "How to Do Case Study Research". School of Nursing Faculty Publication Series, Paper 2. 2009. Available at: http://scholarworks.umass.edu/nursing_faculty_pubs/2.
x H4: A systematic and pervasive abstraction of every financial object as an informational element is neither necessary to develop computational finance applications nor desirable to capture the essence of financial objects computationally, but the triplet <financial instrument or contract properties, trading/negotiation MODE, instantiating time> can constitute an effective abstraction for financial information in computational terms.
H5: The particular arrangement in which financial agents are capable of interact with each other acts itself as an uncertainty solving mechanism which in turn affect the informational dynamics in the system. Therefore, the concept of a computational financial network exists as a way of translating system dynamics into information structures.
The set of hypothesis represent a simple but clear picture of financial systems as potential computational frameworks.
Development of the research work / testing the hypothesis
An analysis of a sufficiently large set of pricing algorithms is a requirement for sustaining any reliable conclusion. There is a plethora of instruments (assets), trading conditions, and pricing algorithms in the financial & business environment. So in order to manage the information available in an organized way, the following methodological framework is proposed:
Two sets will be defined. A set P of m pricing problems P = {P1, P2, P3,…, Pm} and a set A of n algorithmic pricing techniques A = {A1, A2, A3,…, An} is to be produced. The Cartesian product of the two sets P X S produces the universe U (m, n) of possible problem – solution pairs which are the domain of an abstract pricing function (or alternatively, as we will see later, a pricing engine).
Relevant patterns are expected to emerge as a result of this analysis.
After the problem–solution proposition is determined, I searched the articles reviewed for conceptual overlappings, data correlations, independent proposition confirmation, and alternative explanations for the same or similar propositions, methodological and conceptual frameworks or guidelines, even if they were proposed under different assumptions4. This task I consider relevant as to get insight about the model bias that exists behind the algorithms’ design5.
As for facilitating the explanation of the relevant features identified as a result of the patterns detected, the discussion is complemented with “case studies”, both to provide working examples of the algorithms discussed and to present my own proposals as to characterise pricing algorithms I am analysing. At the end, the logical chain of reasoning articles – (pricing problem, pricing
4 As a general remark, I always try to comply with Carl Sagan’s rules for critical thinking (independent confirmation of the facts, look for alternate explanations, quantify whenever possible and justify every link in a chain of arguments, not just most of them). Also worth to mention, Newell and Simon proposed a characterisation of computer science as an empirical discipline, in which each new artefact, e.g. a program, an automata, a platform, a portal, even a protocol, can be seen as an experiment, the structure and behaviour of which can be studied using methods which roughly resemble those of empirical disciplines. Therefore, computer science is concerned with a number of objects which together comprise technologies, but also involve abstract reasoning in the form of philosophies and paradigms which motivate methodological decisions. Sources:
Popova, Maria. “The Baloney Detection Kit: Carl Sagan’s Rules for Bullshit-Busting and Critical Thinking”, https://www.noodle.com/articles/carl-sagans-rules-for-critical-thinking-and-nonsense- detection / https://www.brainpickings.org/2014/01/03/baloney-detection-kit-carl-sagan/. May 6, 2015. Accessed online 25.01.2016.
Newell, Allen and Simon, Herbert A. “Computer Science as Empirical Inquiry: Symbols and Search”.
Communications of the ACM, Vol. 19, No. 3, March 1976, pp. 113-126.
5 It is common practice among the financial community to support their research work with actual market financial data, however, that data cannot be regarded as “naturally” occurring facts in the financial environment, as financial modelling involves, as a rule, manipulation.
xi algorithms) – case studies can be regarded as of a factual, interpretative or evaluative approach, depending on the circumstances.
As for sources and presentation, only documented algorithmic pricing techniques are considered, and the classical algorithmic <<input–processing–output>> scheme is chosen for presenting them Interpreting the results and stating conclusions that can be evaluated independently by others Interpretations are summarized as tables, because they facilitate putting concepts in relation to others. While the validity of the conclusions was always assured, reliability (the degree to which a procedure produces similar outcomes when it is repeated) is, as a general rule, difficult to ensure in the context of social science research. There is no hard evidence to assert that the algorithms analysed here were actually implemented in practice, as there is no way to estimate the degree of penetration of the computational techniques discussed in the real market environment, in part because researchers and market makers might not be the same, and also because traders and other financial agents are not in a position to disclose what specific algorithms and computational techniques they used or are currently using, and how exactly they are using them. But it is safe to assume that many of the algorithms/algorithmic structures reviewed, or at least the ideas behind them, have made their way up to the actual operating computational finance platforms (it is difficult to significantly depart from well-established mathematical finance theory).
No “real-world” applications or ‘demos’ were analysed on detail, as for example testing versions of pricing systems, but the conclusions regarding the scope, potential and characterisation of pricing algorithms and pricing algorithmic techniques remain solid.
0.3 Relevance of the thesis topic
In a study regarding the practice of pricing, the international company Deloitte says: <<As little as 10 or 15 years ago, most prices were set by salespeople, marketers, or product managers as part of their responsibilities. Today, companies are treating pricing as a job in its own right. For good reason: A strong pricing capability, one that uses the multitude of new pricing technologies and tools developed over the past couple of decades, can be a powerful way to bolster a company’s stock price and its bottom line.>>6 Another quote states: <<Aggregated over the total software lifecycle, firms adopting in-house strategies for OTC (over-the-counter, i.e. derivatives) pricing will require investments between $25 million and $36 million alone to build, maintain, and enhance a complete derivatives library>>7.Moreover, <<Not only is it costly and time-consuming to build a full-fledged derivatives analytics library, but you also need to have enough experts to do so. And these experts have to have the right tools and technologies available to accomplish their tasks>>8 (here, ‘tools’ can be taken as pricing procedures). To summarize, the relevance of the topic is described in the following table by topic of interest:
Topic Relevance of contribution
Algorithmic theory Pricing algorithms accounts for a proper sub-field of algorithmic theory, which the thesis attempts to show schematically and contextually.
Education in computer science
The thesis shows that pricing algorithms is a suitable topic for advanced algorithmic courses, with the additional advantage that the algorithmic procedures are much closer to actual economic processes in the real world than usually.
Financial theory By addressing the question about the impact of algorithmic techniques, especially pricing techniques in the financial
6 ‘Is there a career in pricing? An insider’s view of the pricing profession’. Deloitte Development LLC, 2009. Available at: http://www2.deloitte.com/content/dam/Deloitte/us/Documents/strategy/us- consulting-ppm-is-there-a-career-in-pricing.pdf.
7 Ding. 2010.
8 Hilpish. Y. Op. cit.
xii arena, a better understanding of the new computational finance landscape is encouraged.
Emerging computer technologies
Also worth considering is the pricing of distributed computing resources: recent developed technologies such as cloud computing, grid computing, and the internet of things (IoT) among others, raise the question on how to price virtualized computing services.
Business models Pricing techniques are becoming fast important for the new data-driven business models9: firstly, pricing of information plays a role in “information optimization” within environments characterised by large quantities of it (big data); secondly, business forecasting can reach more accurate prediction of prices. <<With large datasets, behaviour or phenomena can be analysed en masse and trends identified that predict future actions>>. Therefore, the impact of pricing algorithms in articulating business strategies is worth considering.
Corporate governance 10 The general setting on which pricing procedures and techniques are applied, is shared by other corporate functions, establishing links between corporate government practices and pricing strategies/procedures. Corporate governance is viewed as a market by herself, and good corporate practices as assets to be “priced” in abstract terms.
9 Under modern data-driven business models, companies are increasingly turning to computer algorithms that can learn from the data they process. Operation of such algorithms starts with a predefined model operate by <<building a model from example inputs and using this to make predictions or decisions, rather than following strictly static program instructions>>. Consequently, there is a growing potential for big data analytics to have an impact of business model definition and strategy implementation. Source:
Bishop, Christopher M. Pattern Recognition and Machine Learning. First edition, Springer, 2006.
10 Corporate governance is defined as the <<set of rules that define the relationship between stakeholders, management, and board of directors of a company and influence how that company is operating.>> At its most basic level, corporate governance deals with issues that result from the separation of ownership and control. At a more evolved stage, corporate governance sets the stage for information management inside and outside the enterprise, and for establishing an institutional controllership system (sistema de control interno, in Spanish), and a procedure to evaluate decisions respect of corporate goals as objectively as possible. According to Boot and Macey, a corporate governance system must accomplish three things: (1) lower contracting costs by providing minority shareholder protection, well defined property rights and default rules and reliable enforcement of such rules; (2) lower agency costs by providing mechanisms for controlling managers; and (3) protect specific human capital investment, or more broadly defined relationship specific investments. But what would then be the relationship between corporate governance and a pricing process? First, empirical evidence suggests that the majority of institutional investors are willing to pay a premium for the shares of a well-governed company over one considered poorly governed, both with a comparable financial situation. As a result, best corporate governance practices may indeed increase the value of companies, and by extension, the stock price. Second, good relationships with customers and suppliers are essential, and those relationships build over internal communication and collaboration within the firm (corporate governance), freeing the pricing process as serving as leverage for the sales department to achieve financial objectives at the cost of price manipulation.
Finally, it is not possible to raise capital outside the firm at a reasonable price unless a corporate governance system that adequately addresses these agency problems is set in place. Sources:
Youssef, M. Tarek. “Corporate Governance– An Overview”. Grant Thornton Egypt.
Gopalsamy, N. A Guide to Corporate Governance. First edition, New Age International, September, 2008. Chapter 1 “Introduction”, pp. 20-29.
Boot, Arnoud W.A. and Macey, Jonathan R. “Objectivity, Control and Adaptability in Corporate Governance”. April, 1998.
xiii Summarizing, my intention was to provide an introductory discussion of pricing algorithms theory, but enough for a setting a working framework on the topic.
0.4 Organization of the Master Thesis The thesis consists of 6 chapters.
Chapter 1, “Introduction”, introduces the topic to the reader presenting in a dual fashion. It covers some general remarks about the financial system and attempt to motivate the reader by presenting some cases in which pricing algorithms have been misused (manipulation of the markets, collusion).
Pricing algorithms are contextualized in terms of their relation to other algorithmic topics, allowing the reader to get a quick “birds-eye” of the objects being studied.
Chapter 2 “Financial and economic foundations for computational applications”, equips the reader with an essential minimalistic economic/financial prerequisite knowledge necessary for the proper understanding of the subsequent chapters, as computational finance is related closely to finance and farther to economics. The discussion gravitates around the axis represented by the relation of the two key concepts in each field: economic scarcity―computational complexity, suggesting that both shape either in a similar way. Further coincidences are identified and discussed, including the natural equivalence of the confirmation of primordial hypothesis: the Efficient Market Hypothesis and P = NP. The financial system is presented with a constructivist perspective (building blocks) and the essential correlation between discrete and continuous views of reality is proposed as the basic template for financial modelling, and consequentially, for that of computational finance.
Chapter 3 “Algorithmics and computational aspects of financial markets” continues the deductive approach toward the topic of pricing algorithms. The fundaments of computational finance as presented as a threesome: scope‒taxonomy―domain. The question of whether or not financial transactions are computable is addressed, the first consideration to be made for automating a system. Then it moves to describing the field of computational finance succinctly but comprehensively: the information modelling paradigms available, the algorithmic techniques used, the architecture underlying the applications and the programming methodologies employed. A comment is devoted to virtualization of finance and the inherent incongruence of the production of artificial markets both as modelling tools and “empirical” testing grounds simultaneously. Two case studies are included. One draws attention to the fact that the unnatural composition of financial instruments yield them impossible to be represented algorithmically. The other proposes descriptions of “grouping” or “agglomerating” concepts in computer science (family, group of techniques, domain, class and paradigm), because I was unable to find one in the literature.
Chapter 4 “Computational price theory” is conceptually the strongest in the thesis. The so-called
“pricing problem” (why should we be worried about pricing at all) is explained through an example.
The concepts of price (a random variable, a realization or instance of a stochastic price process which is a martingale), pricing algorithm (a well-defined procedure implementing a price process for a particular priceable asset in face of its known demand), and computational price theory (the analysis of the reduction of an n-dimensional range by means of the application of pricing algorithms, into scalar prices that provide approximate solutions to resource a specific allocation problem) are defined, and their definitions theoretically supported. Priceable assets are described, as they constitute the domain for pricing algorithms. The derivation of pricing algorithms is presented as the implementation of a pricing kernel into a pricing engine. Finally some important construct form financial theory are explained: the Fundamental Theory of Asset Pricing and the Black‒Scholes formula.
Chapter 5 “Pricing algorithms” focuses on these artifacts in greater detail. First, a logical framework for automated pricing is integrated taking into account the marketability of the items and the class of pricing procedure conveyed. This results in deducing the scope of pricing algorithms putting it in terms of the type of item priced (financial or non-financial) and of their market impact. Commercial
xiv algorithmic pricing is discussed prior to approaching the main discussion topic of financial pricing algorithms. The discussion is structured into an explanation of the internals of the algorithms themselves, and in a review of an actual sample of pricing algorithms, considering implementation methods and the specific problems they attempt to solve.
Chapter 6 “Pricing on the run: pricing schemes for corporate governance” has the purpose to demonstrate that pricing techniques can have significance at a much higher level that just a portfolio or an individual asset; a sound pricing strategy can have significant impact over the initial public offering (IPO) when an enterprise goes public.
1
Chapter I. Introduction
“Life is a game. Money is how we keep score.”
Ted Turner (attributed), The Quotable Billionaire
This thesis is about prices, computational finance and pricing algorithms. Prices are the essence of the material world. Prices are much more than the quantitative/monetary value that will purchase a finite measure of a good or a service. Being prices the consideration given in exchange for transfer of ownership or right to use, there is no doubt they set up the essential basis of commercial transactions11 and provide the means of comparing different goods or services in terms of the satisfaction/utility they deliver to the actual or potential owners or users, as well as in terms of their relative scarcity.
But prices are also an expression of the expectations of the agents about the future and their interpretation regarding the events they observe or that they believe are happening. Therefore prices provide a ground of negotiation for the exchange of goods or the provision of services within a context which is psychological and objective at the same time for the interacting agents, and thus comprising a natural interface for the agents to the markets in order to function properly: <<The stock market is considered essential for economic growth and expected to contribute to improved productivity. An efficient pricing mechanism of the stock market can be a driving force for channeling savings into profitable investments and thus facilitating optimal allocation of capital.>>12
Pricing algorithms have earned a significant reputation within financial field practitioners, but no so much in the academic ground. The topic of pricing algorithms is approached at most only tangentially in the technical literature, and appears mentioned more often in technical blogs or by analysts in different forums, especially in those conversations aimed to divulgate how modern financial markets operate13, or to warn the public against the dangers of computers (i.e. algorithms) “controlling” our lives and the eventual prosecution of individuals unethically profiting from price manipulation.
11 ‘Price’ entry, Business Dictionary, at http://www.businessdictionary.com/definition/price.html.
12 Hasan, Zobaer; Kamil, Anton Abdulbasah, Mustafa, Adli and Baten, Azizul. ” Stochastic Frontier Model Approach for Measuring Stock Market Efficiency with Different Distributions”. PLoS ONE 7(5), May 17, 2012. http://dx.doi.org/10.1371/journal.pone.0037047
13 In a 2013 article regarding the role of algorithms in society, a commentator pointed out that when algorithms are used in problems relating to the social sciences and financial trading, where there is less understanding of what the models and their output should be, and the environment is characterised by volatility, a number of potential situations might arise:
Validation of algorithm performance and potential impacts is limited or impossible (for example, scientists may take years to validate an algorithm, whereas a trader has just days to do so, if she is lucky).
In solving certain problems, it has been observed that there is a large number of agents running very similar algorithms, leading to intertwined behaviour which can trigger phenomena like the
"flash crash" of 6 May 2010, when the Dow Jones Industrial average fell 1,000 points in just a few minutes, only to see the market regain itself 20 minutes later.
Algorithms are now programmed to look for "indirect, non-obvious" correlations in data.
Exaggerating causation when an algorithm identifies a correlation in vast swaths of data can lead to mismanagement and manipulation. For example, shopping habits used as proxies of consumers' health condition, or automatic algorithmic "profiling" used in the legal system.
Another source of concern arises around the way society is structured with regard to data use and data privacy: the use of algorithms to aid policing, as with CRUSCH (Criminal Reduction Utilising Statistical History) algorithms, where the police have reportedly linked some racial groups to particular crimes.
Source: Hickman, Leo. ‘How algorithms rule the world’. The Guardian, July 1, 2013. Available at:
https://www.theguardian.com/science/2013/jul/01/how-algorithms-rule-world-nsa.
2 The chapter first elaborates on the preliminaries of the topic of pricing (algorithm types, contextualization, and information patterns). Then a motivational discussion is presented, involving psychological aspects of computational finance, including two case studies. Finally, different views of financial modelling are explained to complement the introductory discussion. The chapter also includes one appendix.
1.1 Pricing topic preliminaries
As for a preliminary, ‘bird-eye’ view of pricing as a topic, I will elaborate on four aspects: a) an overview of the nature of financial algorithms in general; b) a contextualisation of pricing algorithms within algorithmic techniques: c) briefly discuss pricing mechanisms; and d) briefly discuss financial information patterns.
Algorithms with a “financial personality”: fact or myth?
Computer science and finance had been having a secret affair for a long time, so to speak. Secret not because the “affair” is not public, but because the relationship is blotted out by the very same way the topic is approached. From the economics and finance side, the “algorithmics” of the models as well as the algorithmic nature exhibited by financial transactions14 is overlooked or frankly ignored15; some other times the algorithmic part is addressed, but its’ poor description betrays an insufficient understanding of technical issues. From the computer science side, there is a pervasive allusion to the huge span of software applications and opportunities of IT in the field of finance, but the discussion often stops right there: no further description or examples, let alone the hope of a detailed analysis of computational finance as a subfield of computer science proper. While there is no shortage of literature sources about computational finance, the granularity in which the topic is approached almost always precludes a “higher ground” perspective, with the additional drawback of biases according to the authors’ individual point of view.
Roughly speaking, financial algorithms can be classified as (i) trading algorithms,
(ii) volatility algorithms,
(iii) investing and asset management computer procedures, and (iv) pricing algorithms.
Trading algorithms have evolved into full automatized platforms which require only some monitoring from human traders. These applications provide a template for the activities of hedge funds, for example. The topic is quite interesting, but this is without a doubt the best studied and developed
14 A transaction is a transfer of goods, rights or risk from one agent to another, the most fundamental unit of analysis in economics, finance and organization theory. As an atomic element of larger systems, the way they are organized largely depends on their own characteristics, rather than the characteristics of the more general systems. When transactions occur frequently, at known times and schedules, each time under similar conditions, the transaction realization sequence is called a routine, but when transactions there is no fixed times for transactions, unusual transaction parties may occur and there is uncertainty about transaction realization or even about the possibility to commit transactions, agents undergo into a bargain process about transaction terms, and this situation is called a market. Source:
Bertoletti, P. Course slides for Economics, Organization and Management: ‘Chapter 2: Economic Organization and Efficiency’, at http://economia.unipv.it/bertoletti/didattica/EOM/Chapter2.pdf 15 For example, in a university course I took recently took and that was excellent, one of the books I was require to read was Enough by J. Bogle (Wiley, 2009). One of the author’s objectives was to present a criticism of the financial system, reviewing its evolution and making explicit many flaws and incongruences that happen in the financial markets that can be blamed to some degree for the crisis were are living nowadays. It was shocking for me to realize that the author, which more than once pleases the reading audience with clever and cutting edge insight about the nature of the financial system, not a single time mentioned the impact of computational finance application in modern financial markets. I will refer later to this book in chapter IV.
3 area in computational finance, and therefore more suitable for a more focused study, rather than one intending to generalize concepts across cases.16
Volatility algorithms aim to calculate risk measures for almost any kind of operation, transaction, instrument, portfolio or even agents’ behaviour. The term “volatility algorithm” is better to be understood as an umbrella term for any statistical algorithm aiming to estimate the volatility of observation of any financial variable or time series.
As for investing and asset management procedures, there is no unifying view or predefined scope to rely upon. Investing and asset management is essentially a medium-to-long term activity, depending of the investment/asset management goals pursued. It is the kind of activity financial advisors, holding units, corporate finance managers and mutual funds perform in one way or another (please note: buying stock with the intention to selling it near time in the future is NOT investing).
However, the algorithmic part almost never exercises enough coverage of the scope of investing or asset management operations. Consider for example a group of individuals all whose goal is to build a 401k for each of them. A financial advisor can give them useful suggestions based on their personal financial situation and that of the market(s) they are venturing in, and use some models (algorithms) as an aid to having the job done. But creating a general algorithm that fits all kind of individuals would be an impossible task. Everybody faces a different risk panorama to begin with, and that panorama changes hand in hand with life: a cancer diagnosis, an unexpected promotion or being made redundant at the workplace, getting married or starting a family, buying a house, etc., all changes that alter the way an optimum strategy would be defined. There is, however, interesting research being done under a limited scope basis.17
The main course, pricing algorithms, although being actively developed, do not rest on a working framework that gathers the main properties and characteristics of such kind of algorithms in a way that their structure and implementation can be discussed and evaluated from different perspectives.
How such a framework can be defined is the main research question of this Master thesis. Pricing, as a problem, expresses itself in two different ways: whether to determine if an observed price is correct, and if automated pricing reflects the idea of the “true value” of the asset being priced. The latter will discussed in detail, but the former can be illustrated quickly with the following situation:
when asset prices in a market increase significantly. Rapidly increasing market prices, are a source of concern for policymakers, as it is important to know if the observed increment is being fuelled by fundamental factors or if a price bubble is in the run. Also, it is not enough to know whether a bubble exists or not. They must also estimate how much prices are inflated respect to healthy market figures, which will also provide some intelligence regarding the magnitude of a subsequent potential fallout.
If a bubble grows uncontrolled and burst, it can be as bad as triggering a financial crisis, so the policymaker would feel compelled to take action and reduce the bubble before it is too late. But bubbles are a pattern that arises naturally, and not all bubbles end wrong. It can be even the case that if the agents are already heavily involved with risk-taking positions in a market naturally within an asset bubble pattern, pricking it could cause the very economic contraction they are trying to
16 For an example of how a modern trading platform looks like, please take a look at:
Farrell, Maureen, ‘The computers that run the stock market’@CNNMoneyInvest (New York), July 8, 2013. Available at: http://money.cnn.com/2013/07/08/investing/stock-market-citadel/. One interesting thing that Farrell reports is that <<about 20 programmers create the computer algorithms that decide how to execute each order, and what to send to public exchanges or so-called dark pools.>>.
17 As an example for investing and portfolio management algorithm research, please check:
Agarwal, Amit; Hazan, Elad; Kale, Satyen and Schapire, Robert E. “Algorithms for Portfolio Management based on the Newton Method”. Appearing in Proceedings of the 23rd International Conference on Machine Learning, Pittsburgh, United States, 2006.
4 avoid. So, the question “is the price right?” can be decisive and involves <<more judgment than just whether prices are providing an accurate signal of an asset market’s true value>>.18
Putting pricing algorithms in context
Simply put, this thesis addresses the question of understanding pricing algorithms/ computational price theory as the basic building blocks of computational finance applications and related IT-based business strategies. In financial terms, the central question is to provide arguments to accept or reject the hypothesis that computational finance applications alter or impact markets’ behaviour.
Therefore two profiles regarding the interaction between computer science and finance are figured out. One focusing on the information-processing mechanisms inside the financial system as a relevant factor of the markets’ dynamics, and the other considering those same information- processing elements as informational patterns which set up a framework for analysing financial transactions –understanding how both profiles intersect, and draw conclusions from that. It will be up to the reader to make her own choice of emphasis, according to her requirements, background and preferences, which profile is more important, but in any case, is safe to assume that the conceptualization of pricing algorithms as a theoretical computational problem, would be viewed as an essential one.
Contextualizing pricing algorithms requires identifying similarities, shared problem solving patterns or common conceptual developer tools between them and other types of algorithms. For example, marketplace and allocation algorithms. Marketplace algorithms are a specific kind of algorithms used to optimise behavioural advertisements, individualised promotions and targeted, discriminatory pricing. Therefore, they are related to commercial pricing algorithms, which are used to price commercial goods (merchandise). Allocation algorithms, on the other hand, are a group of diverse algorithms with the common abstraction of establishing a correspondence between two sets of objects. Pricing algorithms relate to them as the function of pricing involves an allocation stage. Since a precise characterisation of pricing algorithms is problem-dependent, the contextualizing task relies more on the scope of different kind of algorithmic constructions. The diagram presents a proposed contextualization of pricing algorithms.
18 Courtois, Renee. “The Price Is Right? Has the financial crisis provided a fatal blow to the efficient market hypothesis?”. Region Focus. Fall, 2009.
5 General pricing mechanisms
Pricing mechanisms may be of three different types. Prices can be 1) fixed by a contract or left to be determined by an agreed upon formula at a future date, 2) “discovered” or negotiated during the course of dealings between the parties involved, which roughly translates as the market conditions determining the price, or 3) calculated. The higher the option number, the more complex the pricing process, the more the uncertainty involved, and the more the information the price embodies.
Pricing mechanisms and techniques lie at the very core of computational finance, so in a sense, they can be considered the articulated link between computer science and financial theory, and their study not only provides a solid ground for the computational finance practitioner to perform adequately, but also offers a unique view of how both sciences interact. For example, theoretical developments like the modern portfolio theory (MPT), the capital asset pricing model (CAPM), and value-at-risk (VAR) all have their foundations in daily stock price data19.
Calculation/ estimation of prices as a price mechanism is the main reason for pricing algorithms20 to exist in the first place, but they might also come as a handy tool for the agents in a price discovery process, and may provide a referential value in the case of contract-fixed prices, so pricing algorithms can be useful whatever the pricing mechanism in operation. While it would be theoretically possible to find application for pricing algorithms in a broad class of economic situations, it is in the field of computational finance where pricing algorithms meet their prime development. As a result, the core of this Master thesis revolves around computational finance, but relevant applications of pricing algorithms outside the field of computational finance are mentioned when necessary.
Financial information patterns
Market dynamics require informational patterns which can be used over and over again in a variety of contexts, in order to develop functional organizational models. The simple fact that financial variables values can be put together as time series, reflects a chronological informational pattern.
Same goes for executing financial transactions, where the transaction can be decomposed into a sequence of steps. In this case, a sequential informational pattern also emerges. These examples, depict simple patterns in which presentational aspects of information are key21. Let’s consider two examples of the nature of informational patterns:
a) Consider culture as a. Informational cultural patterns are considered to develop around structures called memes, which are elements of a culture or system of behaviour that may be passed or shared among individuals by non-genetic means, like imitation, learning or replication.
So, the memetic information structures encode informational patterns which translate into either cognitive or behavioral phenomena, and can be classified according to that.22
b) In computer science, informational patterns develop around data structures. A data structure is a specialized format for both organizing and storing data.23 This dyadic aspect of data structures allows us to think of them conceptually as “packages”.
19 Hilpish. Yves. Python for Finance. First edition. O’ Reilly, 2014.
20 A formal definition of pricing algorithms will be provided later in Chapter 5. For now, let us consider pricing algorithms are the tool take as input a set of features of a priceable item and produce a numerical value which represents a fair price for that item under current market conditions.
21 For more information pattern templates please check:
‘Patterns of Organization’, at http://www.ereadingworksheets.com/text-structure/patterns-of- organization/, and ‘Organizational Patterns Found in Informational Texts’, at http://www.curriculum.org/secretariat/files/Oct25Patterns.pdf, October, 2006.
22 Recchia-Luciani, Angelo N.M. “The Descent of Humanity: The Biological Roots of Human Consciousness, Culture and History”, p 75. In Origins of Mind, edited by Liz Swan, Springer, 2013.
23 ‘data structure’, at http://searchsqlserver.techtarget.com/definition/data-structure. Accessed online 29.04.2016.
6 So, the question is: how a useful and effective characterisation of informational patterns can be constructed for a financial system?
In the case of a financial system, informational patterns exhibit two basic properties:
- generally speaking, they are shared not by means of direct communication between the participating agents, but through financial variables which act as interfaces, such as volumes and prices, and
- they are subject to optimization prior to be used.
These properties make it quite challenging to characterise financial informational patterns. For example, there are aspects of the optimization of the patterns that are situational, i.e. that depend on contingent elements present on a particular point in time or on behaviours displayed by the agents based on their expectations. The “packaging” abstraction is also not well suited for financial information. The information presents itself dispersed across financial instruments and contracts and in addition to that, informational financial patterns might be unstable, because of the inherent uncertainty endogenous to the financial environment itself.
1.2 Computational finance: a motivational entrée to a rugged landscape
The first ideas that usually comes to mind to when the words “computational finance” are heard among the non-technical audience resemble something like “beating the market” through trading;
the abstract concept of financial markets as a source of “infinite wealth”; or the existence of some gurus that possess a “higher understanding” and therefore are able to make extraordinary profits where everyone else cannot24, or that are pulling the strings of the economy behind the scenes with the aid of technology toward dark objectives. But generally all of these ideas can be resumed in the perception of a fundamental ambivalence in the financial system (and of computational finance as natural appendix to it): a minority of happy-go-lucky people getting immensely rich and a blue-collar hard-working majority engaged in a never ending struggle to recover from the impact of financial crises, let alone recurrent news regarding firms’ CEO’s corruption and misbehaviour. While the true nature of the financial environment in general, and of computational finance in particular, is somewhat beyond the grasp of the mere uneducated mortals, some of the former ideas, although naïve, might capture nevertheless some relevant features of the financial system.
Recently, the idea of a mythical money-making algorithm set in the imaginary of the people is being exploited in many ways. One of the most visible is the sheer amount of offers to make money out of
“trading” binary options25: mind-blowing algorithms which the platform runners in a sudden fit of
24 For example, take the 2011 sci-fi thriller “Limitless”, where the protagonist, with the help of a mysterious pill that enables the user to access 100 percent of his brain abilities, becomes an astounding financial wizard, and thus popularized the idea that success in the financial markets consists in the ability to detect extremely well hidden patterns and then tune up a new clever algorithm to take the necessary advantage. A post in a related forum proposes: <<Without going into too much detail: The stock market in general, individual sectors, and individual corporations can be predicted mathematically, through pattern recognition and the ability to mathematically describe the patterns. You must be able to mathematically describe the progression of wave-like patterns over time, and then you can predict the timing and significance/degree of high points and low points during rising and falling periods. If you can do this, there should really be no limit to the amount of success you can have. >> Sources:
Limitless IMDb card at http://www.imdb.com/title/tt1219289/. Accessed online 15.04.2015.
Limitless: Stock Market Can Be Predicted Using Equations. ‘The Journey’ blog. Posted on December 31, 2012 at http://www.abovetopsecret.com/forum/thread913573/pg1. Accessed online 15.04.2015.
25 Technically, a binary option a type of option (financial contract) in which the payoff is structured to be either a fixed amount of compensation if the option expires “in the money” (meaning that the option is worth money so the holder can turn around and sell or exercise it) or nothing at all if the option expires “out of the money” (meaning that is worthless). Investors may find binary options attractive because of their apparent simplicity: it involves only a guess. For example, the guess as whether the price of XYZ Company will be above 1 euro tomorrow before the market closes is a
