Abstract
The mispricing of the deep-in-the money and deep-out-the-money generated by the Black and Scholes model is now well documented in the literature. In this paper, we discuss different option valuation models on the basis of empirical tests carry out on the French option market. We examine methods that account for non-normal skewness and kurtosis, relax the martingale restriction, mix two log-normal distributions, and allows either for jump diffusion process or for stochastic volatility. We find that the use of a jump diffusion and stochastic volatility model performs as well as the inclusion of non normal skewness and kurtosis in terms of precision in the option valuation.
Highlights
The failure of the Black and Scholes [1] model to provide correct valuation is attributable to the parsimonious assumptions used to derive the model
This empirical literature has proved the stochastic nature of stock return variances and their correlation with security price levels shoing that returns are both skewed and leptokurtic
Corrado and Su [13] derive and test empirically a European option pricing model that extends the [1] model to take into account for non-normal skewness and kurtosis in the distribution of stock returns
Summary
The failure of the Black and Scholes [1] model to provide correct valuation is attributable to the parsimonious assumptions used to derive the model. Observed moneyness biases constitute evidences against the hypothesis that asset returns are homoskedastic and normally distributed; this gave an impulse to the development of option pricing models for alternative processes. Derive a model in series expansion form allowing for instantaneous correlation between stochastic volatility and the stock price. Corrado and Su [13] derive and test empirically a European option pricing model that extends the [1] model to take into account for non-normal skewness and kurtosis in the distribution of stock returns. The skewness and kurtosis coefficients are estimated simultaneously along with the implied standard deviation They find that the adjustments for skewness and kurtosis are effective in removing systematic strike price biases from Black-Scholes [1] model for S&P500.
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