محدودیت ضریب اطمینان برای مدل های داده کاوی از گزینه های قیمت ها

Non-parametric methods such as artificial neural nets can successfully model prices of financial options, out-performing the Black–Scholes analytic model (Eur. Phys. J. B 27 (2002) 219). However, the accuracy of such approaches is usually expressed only by a global fitting/error measure. This paper describes a robust method for determining prediction intervals for models derived by non-linear regression. We have demonstrated it by application to a standard synthetic example (29th Annual Conference of the IEEE Industrial Electronics Society, Special Session on Intelligent Systems, pp. 1926–1931). The method is used here to obtain prediction intervals for option prices using market data for LIFFE “ESX” FTSE 100 index options (http://www.liffe.com/liffedata/contracts/month_onmonth.xls). We avoid special neural net architectures and use standard regression procedures to determine local error bars. The method is appropriate for target data with non constant variance (or volatility).

Data mining and computational methods such as artificial neural nets are increasingly used in finance. They provide an alternative non-parametric model of option prices, out-performing the Black–Scholes (BS) model [1], [2], [3] and [4]. These data mining methods are often generalisations of better known non-linear regression techniques. Confidence in the reliability of models and predictions is a key issue in finance. However, while techniques of statistical inference are well defined for the parametric regression methods traditionally employed in financial modelling, this is not the case for the non-parametric data mining techniques. Consequently, there is an absence from the literature of statistical hypothesis testing [5], and models are evaluated on summary criteria such as mean squared error and R2R2. Also, prediction and confidence intervals are rarely constructed for option pricing models estimated using these techniques. In our work on option pricing, we have found that when input data is partitioned by moneyness/maturity, model price predictions may be unbiased for some partitions yet biased for others. Examination of pointwise prediction intervals is thus a necessity to obtain a fuller picture of model performance than is given by single summary statistics or hypothesis tests. We seek a method which is generally applicable, and can be used with any regression technique of sufficient flexibility. In this paper we describe a robust method for determining prediction intervals for neural nets and related techniques. We have tested the method empirically using a standard synthetic data set, and compared it with a method restricted to neural nets [6]. Here, our method is applied to obtain prediction intervals for pricing options, using a data set of 14,257 LIFFE European style FTSE 100 index `ESX' options [7]. Our method uses standard regression procedures to determine local error bars. It is appropriate for target data with non-constant variance (or volatility).

This paper describes a robust method for determining prediction intervals for models derived by non-parametric forms of non-linear regression. The method can be used with general purpose modelling tools and is not restricted to application specific software. We have demonstrated its utility by constructing prediction intervals for option prices estimated using neural nets and shown their width is a much better indicator of model quality than summary statistics such as R2R2. The method is also applicable to any comparable regression technique of sufficient flexibility.