Neural Net Modelling in Financial Engineering of Options

by Jerome Healy, Longchuan Xu, Maurice Dixon, Fang Fang Cai, Brian Read and Brian Eales

Financial options play a key role in the risk management carried out by financial institutions. As a consequence, their pricing and hedging against adverse market movement is a major challenge for loss avoidance. Although standard options are regulated by the exchanges, exotic options are traded over-the-counter. Neural networks provide a powerful way of deriving models from traded data that are free from most financial modelling assumptions.

A standard call (put) option gives the holder the right but not the duty to buy (sell) an asset on or before a future date at a price specified now. This enables the holder, for a premium, to hedge against adverse asset price changes while benefiting from favourable movements.
The Financial Market Modelling project aims at developing a computational framework with techniques appropriate to accurately predicting option prices from exchange data, and to hedging their movement against adverse movements. This would enable issuers of options to buy and sell financial instruments to change their exposure as the market moves.

The research is grounded in the underlying data-mining program of the Business and Information Technology Department of CCLRC. Recently a project grant was obtained from HEFCE by London Metropolitan University, Londonmet, to establish a Financial Modelling Research Base at Moorgate in the City.

There is now an abundance of high- and low-frequency data available from various exchanges. Analytic models have tended to assume an underlying log-normal pricing distribution following Black-Scholes-Merton. Numerical models free from this and other constraints can be extracted from traded data.

The aim of the project is to provide a systematic framework for the generation of numerical models and predictions/forecasts from option market data. This will be done by combining established modelling approaches with diagnostic techniques from econometrics.

The development framework was CRISP-DM (CRoss Industry Standard Process for Data Mining). It was specialized to option market applications. Neural nets were deployed to provide regression models that are twice differentiable; also they are used to provide self-error estimates. Linear regression and Monte Carlo simulations supported the investigation. Standard commercial database, spreadsheet, and data-brushing tools were linked to a data-mining workbench, SPSS Clementine and to the econometric tool eViews from Quantitative Micro Software.

Figure 1
Figure 1: Prediction Bands for Synthetic Example - y(x) is the true regression for a benchmark synthetic model; d represents the target data points generated by adding a known noise function to it. d* is the estimate of the target. L and U are the true upper and lower prediction intervals while L* and U* are the approximate prediction intervals obtained from the prediction for the variance (squared error).

Initial work concentrated on demonstrating high accuracy (R2>0.99), but avoiding over-fitting, using neural nets for pricing standard options with fixed expiry dates from daily data. These had been traded as ESX options on the London International Financial Futures and Options Exchange, LIFFE. An important advance was the development of a practical method for obtaining, for unknown targets, confidence of prediction intervals. It uses the capacity of a neural net to model the joint probability distribution of a function value and point squared error. The method is robust to variable error bars. Its application to a synthetic benchmark problem is shown in Figure 1, where there is good signal recovery from very noisy data. Since second derivatives of neural nets can be determined, it is possible to obtain an important probability distribution, the risk neutral density (RND). This means that that forward expectation of an asset price can be used to aid in setting a measure of value-at-risk. The extension to early exercise put options, SEI, is shown in Figure 2.

Figure 2
Figure 2 SEI Put Option RNDs - One-Month Forecast of FTSE 100 Level. One-month forecasts of the FTSE 100 closing price from the extension of RNDs to SEI (American) put options that can be exercised early. The forecast values (red line) are the medians of the RNDs. The heavy black dashed line is the FTSE 100 closing price one month (17/18 trading days) later. The dotted green and blue lines are ±2 standard deviation (≈ 95.46%) confidence intervals. The true values lie within the confidence band in all cases.

Future work will include over-the-counter (OTC) options, which are priced on the basis of a direct contract between option buyer and seller. These are not exchange regulated and the prices are not publicly available. In addition, some OTC options have a discontinuity where the value changes to/from zero if the asset touches a value called the barrier. Barrier options pose specific problems as hedging depends on the value of the gradients close to a discontinuity.

The approaches developed here have been applied to an environmental application in the recent ERCIM-managed project, TELEMAC. The visualization approaches applied in TELEMAC have been shown to be very helpful for the financial data inspection.

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Please contact:
Maurice Dixon, LondonMet, UK

Simon Lambert, CCLRC, UK
Tel: +44 1235 445716