Histogram-based interest point detectors

1   Introduction

The idea of a machine that can learn from its own interactions with the world has been one of the driving forces behind artificial intelligence research since its inception (^{Turing, 1950}). The most powerful form of this grand challenge is an android, a robot shaped like a human, which could master new skills and abilities by interacting with another person. This machine would be able to exploit the knowledge and assistance of other people to carry out specified tasks, would recognize and respond to the appropriate human social or environmental cues, and would use the natural social interfaces that people use with one another. In a stock market situation, which is of interest here, these machine requirements are less stringent, as the interfaces are or can be made more mechanistic. For instance in stock market on–line trading, interactions involving humans are almost entirely eliminated. Environmental cues in well structured textual and well data forms are largely available on the Internet. Furthermore, it is claimed in this paper that the ‘random walk’ type, ‘ill-structured’ behaviour of the stock market can be better countered through the use of derivative instruments, such as puts to control the effects of a downward movement of underlying stock prices, and calls to allay the effects of an upward movement. With this assumption of a man made mechanistic world, this paper expands the previous line of research on DSS contribution to ‘ill-structured’ decision making by claiming possible full automation of the process rather than simply as a supporting system. This stand forms part of a continuing debate, sparked initially by Herbert Simon, that a thinking and creative machine, in our case the Virtual Decision Maker (VDM), can be used in place of humans, even in the case of ‘ill’ structured decision processes. The idea of VDM for applying complex hedging strategies is further reinforced by known results of studies on human behavioural and cognitive issues.

The paper is organized as follows. In Section 2, we introduce the problem of hedging, in terms of information processing requirements. In Section 3, we justify the idea of the Virtual Decision Maker as a solution to mitigate the behavioural biases, and to overcome the cognitive limitations, of human decision makers. The various components of the VDM as a network of collaborating and negotiating artificial agents are presented in Section 4. We conclude in Section 5 with a discussion of the merits of full automation, as offered by VDM, and mobility and trust issues that emerged from the study.

2   The stock market hedging strategies

In stock market trading, a portfolio approach is generally considered as an effective way to increase returns while better controlling the risk (^{Markowitz, 1952}). Today, experts in stock market trading use derivative instruments, namely options, as part of the portfolio

The spectacular growth in the use of derivatives to manage risk has been one of the most significant recent developments in the financial markets. However huge losses from the use of derivatives have made many investors very wary to the point that some have limited and even eliminated the use of derivatives in their portfolio. The stories behind the losses emphasize the point that derivatives can be used for hedging, speculation or arbitrage. Though individual motivations for the use of options are quite sparse, most losses and mishaps reported conclude on their inappropriate use as a vehicle for speculation rather than a very efficient way to manage risk. (^{Hull J, 2002}). In this paper we assume options use as part of strategies that make it possible to achieve high returns with minimum investment while controlling the risk. We also claim that, with the technological advantage, a portfolio with derivatives instruments offers a much higher diversification that a portfolio with stocks only.

Discretionary buying or selling of options, in the form of puts and calls at a specific striking price for a given time horizon, are among the determinants of the degree of risk of the portfolio. A rational choice of a strategy that involves both a stock and its derivatives requires a lot of calculations that take into account not only fundamental market factors, such as interest rate, ROI objective and theoretical statistics such the so called Greeks indicators with Delta, Gamma and Theta based on the well known Black and Schooles option valuation formula, but also margin and equity ratio requirements imposed by the regulatory agencies and the broker. The metrics to assess the effectiveness of an option based strategy can be based on both the traditional economic approach, whereby portfolio selection consists of optimization over a time horizon dictated by standard options contracts, and the more modern portfolio theory that suggests a single period mean variance or risk approximation. Although many options strategies can be imagined by combining the elementary derivative instruments, in the following we will consider only a market-neutral strategy favoured by the authors with a Delta indicator = 0. Delta is a measure of the rate of change in an option's theoretical value for a one-unit change in the price of the underlying stock. The attachment contains the impacts of each of strategies used in the experimentation, with their respective rewards and compensatory factors. As an example, if we assume that the stock plummets, the investor, with his long Put position, will be able to exercise the Put to dispose of the stock above market value, thus limiting potential damages. On the other hand, if the stock rises considerably, the investor participates to the extent allowed by the covered call position. By repeating this simple procedure, it is possible to attain positions in a very large number of securities. In practice though, the broker will usually want to protect his position by imposing a net minimum equity to securities ratio (E/S) and a positive margin. There are several strategies that could contribute to the E/S ratio and margin, such as the Short Straddle used in our illustrations, but not without additional risk. In short, each addition of options to the strategy will compensate for a weakness while at the same time managing the risk

The following is a typical example of a well balanced option strategy close to Delta = 0 for the EMC stock (Figure 1)

Figure 1:Figure 1:

This partial portfolio position contains 10 contracts (Covered Calls), accounting for a Delta of 270 ((1.73) *1000), 2 Short Straddles that contribute −74 (200*(−.73+.36)), and 10 protective Puts that contribute −200 (10*.20). In looking at the portfolio from the decision perspective, we see it now represents a well structured engineering type of process that requires only systematic adjustments over time. The added granularity offers more opportunities for opportunistic arbitrage trading. Furthermore, the system frequency can be regulated by scheduling tasks with, at one extreme, low opportunistic frequency to react to major changes only, or at the other extreme, high frequency for day trading.

3   Justification for a Virtual Decision Maker

Because the decision making task is more structured, it is also more programmable. In our reactive Delta = 0 approach, the system will recommend a strategy that rebalances the Delta's while contributing to the Net Value. Consider as an illustration the following decision table (Table 1):

The table above shows recommended choices of strategies, for a given direction of stock price movement, and it's Delta.

While the computing required for assessing an option based diversified portfolio is by itself a justification for a technology based decision support system, we are also considering human factors as additional argumentation for technological support. This paper expands our research on DSS contribution to ‘ill-structured’ decision making by claiming that a Virtual Decision Maker (VDM) technology can be used in place of the human decision maker, rather than simply as a decision support system for him. The study tries to validate the idea of the man-made, mechanistic world as being eligible for a Virtual Decision Maker (VDM) in applying hedging strategies. The grand challenge of building machines that can learn naturally from their interactions with people raises on one side many moral questions but on the other side it finds its justification in human factors including behavioural considerations, cognitive limitations of humans and decision style differentiation in regards to risk.

Behavioural issues: overconfidence

^{Barber&Odean (2000)} claimed that clients who switch to on-line trading tend to perform more poorly than the market, mainly because they tend toward overconfidence. The same authors explore the role of three factors, (i) self-attribution bias, in which the investors consider themselves the source of their own success, (ii) illusion of knowledge, in which investors fail to distinguish the overwhelming amount of data available from information, and finally, (iii) illusion of control, in which investors who actively participate in a “hands on” on-line manner by entering orders directly at a keyboard believe they have an effect on the outcome of their investments. Heaton (2001) showed that the assumption of overconfidence provides a unifying framework for managerial incentives to over invest given (perceived) financing constraints. Other measures of overconfidence, based on late option exercise and habitual stock purchases, confirm these results. Because individuals expect their behaviour to produce success, they are more likely to attribute outcomes to their actions (and not to luck) when they succeed rather than when they fail. This self-serving attribution of outcomes, in turn, reinforces individual overconfidence.

Cognitive limitations

Cognitive limitations are at the center of the justification of traditional decision support systems in case of ‘ill structured’ decisions processes. In stating that humans are information processing systems, it is argued that human cognition consists of three connected but independently descriptive parts: a cognitive architecture, a system of representations, consisting of symbol structures, and a set of manipulations, computations, or operations on these symbol structures (Posner, 1989). To overcome its cognitive limitations, the human as an intelligent agent subdivides its task into subtasks to the level that remains within the limitations of its cognitive architecture. Our options strategies decision process redesign is largely based on these types of considerations, with a resulting workflow of collaboration or negotiation involving agents to resume eventual conflicts.

Decision Style

The stock market is the result of equilibrium, in which some investors buys while others sell, according to their different risk-aversion preferences. While this applies equally to options, the demand for buying or selling call/puts could be explained by utility functions or, to a greater or lesser extent, the degree to which investors face one another, and background risks (revenue, professional situation, past successes and failures). In our case the behaviour can be detected in the investor's choice of sell or buying of Straddles. In making the parallel with existing research, investors with low background risk sell straddles, whereas investors with high background risk buy the same straddles. With that in mind, we can almost state the role of options in the selected strategies as being use for hedging, arbitrage or speculation. Although the main objective of the VDM is to adapt its strategies to the user's risk preferences, in this initial version, only strategies based on Delta equals zero are considered.

4   Components of the VDM

To be effective in a stock market situation, the VDM needs some specialized features. Starting with a rich set of perceptual abilities to recognize cues in market data to detect when the context is appropriate for trading. Next is a range of cognitive skills to exploit a knowledge base typically used by an expert professional trader. More specifically VDM should be able to formulate and assess strategies at its disposal and to produce messages to indicate its final trading choice. In its more robot-like abilities, the VDM should not only be able to feed stock market data as input to its knowledge base, but also be able to request execution of the choice by presenting it in the same format as required in human-originated trading. The VDM should perform these automated tasks in such a way as to succeed in a form of the well-known Turing Test. In other words, the broker or his system should not be able to distinguish if it is a human or a machine that is originating and formulating the incoming transactions. Finally, the VDM should also be able to learn from its past experiences by continuously receiving feedback and evaluating the progress of its portfolio.

The agent follows personalized decision heuristics, including alarms, possibly to a remote device, in the case of an extreme or unplanned scenario. While many documented artificial agents contain a statistically based forecasting model and a few business inferential rules, they are incomplete for our purpose because:

• They are limited to stock trading only
• They are intrusive in that, the system interface requires an officially-sanctioned closely-coupled communication-based connection to the broker
• They are pro-active, that is they rely mostly on the questionable precision of the forecast of the stock's price, as opposed being reactive.

To further improve the analogy of the VDM with a human, and justify the terminology of the Virtual decision maker, we have analysed and designed the input, expert processing, and online automatic order tasks that parallels the judgement tasks of the human decision maker. The following describes the various intelligent agents are part of the VDM,

Retrieving Stock Information

The task of the perceptual system is to convert complex sensory signals into representational states within this model. Two types of data are required, namely the market and the portfolio data

A stock market data

extraction agent, in our case a commercially available Excel viewer with a direct feed of market data via the Internet, posts the data on a type of Blackboard) that is used by the other intelligent agents as required. (^{Nii Penny, 1989}) Its task is to filter selected data needed for the decision making process from a wide range of information sources and access protocols invisible the user. However the user can specify his information needs on a rather high-level of abstraction (stock codes, news,) and the agent will autonomously collects and combines the desired information from multiple information sources in the network,.

Portfolio data

is extracted automatically from the portfolio account statement prior to the trading day along with the information on equity and margin available. The input module renders the information in terms of Covered Calls, Straddles, Long Puts and Naked Option positions as shown hereunder, (Figure 2)

Figure 2:Figure 2:

In this example the system assesses the current situation and identifies the following strategies: 24 Covered Calls, 9 Short Straddles, 3 Naked Calls and 10 protective puts with a stock at the time of observation at $29.75 up. 48 from the day before.

A convenient division in reasoning comprises analysis, change and synthesis task taxonomy.

Based on that classification, option strategy formulation is a synthetic task that consists of combining stock and derivative instruments in different ways to form strategies such as covered calls, straddles etc. They are over thirty generic and frequently used options strategies with some properly called Synthetic that represent a strategy involving two or more instruments that has the same risk-reward profile as a strategy involving only one instrument, and some called Combination that represent a strategic position involving out-of-the-money puts and calls on a one-to-one basis These basic synthetic positions can be further expanded by making combinations across stock or index futures. The combinations increase the number of possibilities for hedging thus making more probable an opportunistic trade or an arbitrage

We could consider that synthetic tasks create an artefact or many artefacts that could be used in various portfolio and market scenarios including extremes such a stock market crisis. Thus an assessment of the situation is required.

The assessment agent

In our neutral stand, the portfolio is systematically affected by a market movements, reinforcing the need for a task to monitor change This is better accomplished by following a Delta metrics using a ‘Greek’ agent. (Table 2)

It can be noticed that the overall MSFT strategy is positioned for an up-movement (Delta positive), while the overall VRSN strategy would succeed in the case of a Down movement of the underlying stock. Both are undesirable given the neutral strategy used in the portfolio. By selling some stocks, buying long puts, or acquiring a short Straddle, it is possible to adjust the corresponding Delta at a profit.

In most cases the adjustment could contribute positively to the equity as well as to the margin or to the equity ratio, depending what is required. The selected strategies for each stock are posted on the blackboard for consideration by other agents.

The reasoning Agent

The reasoning agent implies an analysis task to maximize the objective while respecting the constrains. At its foundation is a linear programming model with strategies as variables, and Delta = 0 for each individual stock, and margin and the equity ratio as overall constraints. The optimisation agent aims at the portfolio metrics as opposed to per stock assessment by the ‘Greek’ agent. The objective function optimization determines the intensity (volume) of each strategy to maximize Net Value of the portfolio. In the current version on Excel, the system uses the popular Solver add-in functionality. The results are posted on the blackboard leading occasionally to a conflict with results posted by the preceding agent.

The Central Management/ negotiation Agent

The management/negotiation agent acts as a proxy for the decision maker. It has as a specific rule based environment, supporting the execution of its decision making. At one extreme it helps to reduce the amount of communication between the agents. For instance, it can initiate and change stop-profit, limit, or stop-loss orders bypassing all the preceding agents. At the other extreme, it can assist in the communication between the human decision maker and the various autonomous intelligent agents. Using inferential rules, the management agent is capable of formulating arguments and counterarguments in order to decide whether to perform an action or not. Among other things, it takes into account decision makers risk style and the direction of the market (up or down) to recommend a final strategy. In its current version, it uses a knowledge based agent using an Expert System Shell that acts as a compromising actor. In addition to market and decision maker related knowledge, it takes into account some expert rules and the information placed on the Blackboard, including the conclusions of the two previous agents considered as facts. If there is a conflict, the various agents have to negotiate or collaborate using information posted on the blackboard and/or by interacting with existing agents. If the conflict between the various intervening agents persists, then the management agent applies predefined negotiation rules. In extreme cases, a mobile communication agent, to be designed, would communicate with the decision maker for a final decision. If he cannot be reached, the decision is either abandoned, or negotiation continues, using with discretion some existing Meta rules. For instance it is possible that despite obvious opportunities, attempting to follow the market-neutral strategy recommendations would not allow any action to take place. In that case, a Delta is allowed to deviate slightly from zero, opening the way to many new, potentially conflicting strategies.

At the heart of the management-negotiation agent is a VB based knowledge based system Shell (Visual Rule Studio) that interacts with an Excel sheet containing the blackboard and the other agents.

Output: execution agent

VDM as a network of cooperating and negotiating intelligent agents' that can exploit automated on-line trading services at any time and any place without the physical presence of the decision maker. The execution agent completes the cycle by posting the selected decisions through the broker's standard (“user-friendly”) interface. Two alternatives were investigated for implementation: first a tight communication system link to the broker's Web server and second with a program that emulates the key board and mouse movement needed to specify the details of the final decision. The latter solution was selected as less intrusive, and independent of the broker's server API's and middleware, assuming he even offers them. As a result, the current version of the VDM is capable of executing the order by ‘physically’ specifying the recommended strategy directly to the interface provided by the broker and is perfectly adaptable for other competitive trading environments. This complementary feature that completes the full automation cycle was implemented in VB script.

5   Conclusions

Even though our VDM has up to now clearly outperformed the various indexes in both real lives over a one year period trading as well as in simulated trading we cannot conclude that this is a statistically significant result. Prior, many well documented failures would contradict that conclusion. Though the financial performance will remain the final indicator of the success or failure we can in the interim discuss the idea of automation on the basis of formally requested opinions. This more interpretative approach has led to some interesting remarks by the experts or potential users. First stock picking as the underlying security for the option strategy was considered key. Data for classic fundamental as well as technical analysis was requested as part of the input agent task. We have associated this to an anchoring phenomenon. The reasoning process, including the optimization, and negotiation was accepted at face value without questioning the logic, rules, and quality of data used. We have associated that with the cognitive effort that would otherwise have been required to reach a decision. Contrary to expectations, the automation of the execution of final decision was not perceived as an added advantage; most would prefer that this remain a human supervised task. We have associated this with the issue of trust between agents and end users. Trust as a relationship between clients and VDM could be determined by the amount of non discretionary money they are willing to give to these agents to invest on their behalf. While it would be easy for the VDM to pass the Turing test, its acceptability as a fully automated machine needs further investigation. To that end, a Web based implementation with the possibility of access from a mobile device seems to be at this point one of the critical features that ought to be added. The more scientific experimentation has to be continued to the expiration of all options to test both the superiority of the VDM as well as the merits of the neutral strategy, a personal preference.