This article develops an option pricing model and its corresponding delta formula in the context of the generalized autoregressive conditional heteroskedastic (GARCH) asset return process. the development utilizes the locally risk-neutral valuation relationship (LRNVR). the LRNVR is shown to hold under certain combinations of preference and distribution assumptions. the GARCH option pricing model is capable of reflecting the changes in the conditional volatility of the underlying asset in a parsimonious manner. Numerical analyses suggest that the GARCH model may be able to explain some well-documented systematic biases associated with the Black-Scholes model.

The garch option pricing model

This paper discusses the commonly used methods for testing option pricing models, including the Black-Scholes, constant elasticity of variance, stochastic volatility, and jump-diffusion models. Since options are derivative assets, the central empirical issue is whether the distributions implicit in option prices are consistent with the time series properties of the underlying asset prices. Three relevant aspects of consistency are discussed, corresponding to whether time series-based inferences and option prices agree with respect to volatility, changes in volatility, and higher moments. The paper surveys the extensive empirical literature on stock options, options on stock indexes and stock index futures, and options on currencies and currency futures.

Testing Option Pricing Models

This paper illustrates regression and Kalman filtering methods for estimating the time-varying term structure of volatility expectations revealed by options prices. Short- and long-term expectations are estimated for four currencies using daily PHLX options prices from 1985 to 1989. Throughout this period, there were important differences between shortand long-term expectations. The slope of the term structure changed frequently and there were significant variations in long-term volatility expectations. The expectation estimates can be used to value OTC options, to improve hedging strategies, and to test the hypothesis that the options market overreacts.

The term structure of volatility implied by foreign exchange options

Neural networks have shown considerable successes in modeling financial data series. However, a major weakness of neural modeling is the lack of established procedures for performing tests for misspecified models, and tests of statistical significance for the various parameters that have been estimated. This is a serious disadvantage in applications where there is a strong culture for testing not only the predictive power of a model or the sensitivity of the dependent variable to changes in the inputs but also the statistical significance of the finding at a specified level of confidence. Rarely is this more important than in the case of financial engineering, where the data generating processes are dominantly stochastic and only partially deterministic. Partly a tutorial, partly a review, this paper describes a collection of typical applications in options pricing, cointegration, the term structure of interest rates and models of investor behavior which highlight these weaknesses and propose and evaluate a number of solutions. We describe a number of alternative ways to deal with the problem of variable selection, show how to use model misspecification tests, we deploy a novel way based on cointegration to deal with the problem of nonstationarity, and generally describe approaches to predictive neural modeling which are more in tune with the requirements for modeling financial data series.

Neural networks in financial engineering: a study in methodology

Publisher Summary This chapter focuses on the central empirical issue in option pricing, which is whether the distributions implicit in option prices are consistent with the conditional distributions of the underlying asset prices. Tests of consistency are almost invariably conducted within the framework of a particular distributional hypothesis, and therefore to some extent involve a joint test of consistency and of that distributional hypothesis. The most common framework by far has been the geometric Brownian motion hypothesis underlying the Black-Scholes model. This one-parameter model has been used extensively to examine whether volatility assessments inferred from option prices are consistent with the conditional volatility of the underlying asset price. Results have been mixed: implicit volatilities from most currency options are relatively unbiased forecasts of future currency volatility, whereas substantial biases have been found in implicit volatilities from stock and stock index options. There also seems to have been substantial evolution in the sophistication of option markets. Results including the early years of options markets typically involve more noise (for example, more arbitrage violations) and a greater divergence from the time series properties of asset prices and implicit volatilities than found in studies from later periods.

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This paper examines the pricing of S&P 100 calls using 14 months of transactions data. We find that market prices of S&P 100 calls differ systematically from Black-Scholes values. The biases in Black-Scholes model prices are both statistically and economically significant and correspond to biases that arise if market prices incorporate a stochastically changing volatility of the index.

https://www.jstor.org/stable/pdfplus/2331406.pdf

Transaction Data Tests of S&P 100 Call Option Pricing

Rogalski-Tinic have reported a monthly pattern in ex post stock return variances that differs between small and large market capitalization firms. Maloney-Rogalski find that option prices reflect these monthly patterns ex ante. This study extends Maloney-Rogalski's work by devising an expiration-specific weighted implied standard deviation (WISD). It is found that: i) the monthly patterns in one-month WISDs are basically similar to the monthly patterns in ex post variances detected by Rogalski-Tinic for both large and small size firms, and ii) use of expiration-specific WISDs, as opposed to standard composite WISDs, results in improved performance of option pricing models.

Aamir M. Sheikh

Papers

Transaction Data Tests of S&P 100 Call Option Pricing

Time varying volatilities and calculation of the weighted implied standard deviation