Efficient Option Pricing Under Levy Process: Empirical Evidence From Taiwan

摘要

This paper presents an efficient option pricing method for calibrating exponential L(e)vy models to a finite set of observed option prices. This paper shows that the usual formulations via non-linear least squares and also reformulates the calibration process into a problem of finding a risk-neutral exponential Levy model which reproduces the observed option prices and has the smallest possible relative entropy with respect to a chosen prior model. This approach allows us to reconcile the idea of calibration by relative entropy minimization with the notion of risk-neutral valuation. With discussion the numerical implementation of our method using a gradient-based optimization algorithm and show by simulation tests on various examples that the entropy penalty resolves the numerical instability of the calibration problem. Our tests reveal a density of jumps with strong negative skewness. While a small value of the jump intensity appears to be sufficient to calibrate the observed implied volatility patterns, the shape of the density of jump sizes evolves across maturities, indicating the need for departure from time-homogeneity. Finally, we apply our method to data sets of Taiwan Stock Index Options and discuss the empirical results obtained. Our efficient method would provide a brand new perspective for option pricing. When dealing with options and particularly hedging is a topic at least as important as pricing if no more. Giving the risk produced by a derivative product, being able to calculate and control this risk is the purpose of a lot of models.