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RESEARCH PRODUCT

Impact of Stock Price Jumps on Option Values

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Many empirical papers document the fact that the distribution of stock returns exhibits fatter tails than would be expected from a normal distribution. This might explain some of the pricing biases of the Black/Scholes model, which is] based on a normal return distribution. Given this result, alternative option pricing models should be based on one of the following three classes of return models: (1) a stationary process, such as a paretian stable or a student’s t-distribution, (2) a mixture of stationary distributions, such as two normal distributions with different means or variances, or a mixture of a diflusion and a pure jump process, or (3) a distribution such as a normal distribution with time- varying parameters. Although any of these choices could improve on the fit of the normal distribution, only a few are economically as appealing as the mixed jump diffusion model. According to this model, the total change in the price of a stock is equal to the sum of two components: (1) the normal fluctuations in price due to new information that causes only marginal changes in stock’s value (‘diffusion component’), and (2) the abnormal price changes due to the infrequent arrival of new information that has more than a marginal effect on price (‘jump component’). This mixed jump diffusion model was first studied by (Press (1967)) and incorporated into the theory of option valuation by Merton (1976a). Although a considerable number of papers report a statistically significant jump component in stock returns as well as in index returns (Jarrow/Rosenfeld 1984, Ball/Torous 1985, Akgiray/Booth/Loistl 1989, Beinert/Trautmann 1991), few papers have investigated the effect of jumps in the underlying stock price process on option values. In the first published empirical paper on this subject, (Ball/Torous (1985)) find no operationally significant pricing differences between the Black/Scholes model and Merton’s idiosyncratic jump risk model when pricing options on NYSE stocks. By contrast, (Bates (1991)) finds that a systematic jump risk model fits the actual data markedly better than the Black/Scholes model in the case of the transaction prices of S&P 500 futures options.