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.