An Application of the Empirical-Distribution-Based Model on the Implied Volatility of Taiwan Warrants

Abstract

Theories such as jump process, stochastic volatility, the GARCH model, and implied risk-neutral distribution have been developed to account for the volatility smile. Nevertheless, none of them succeeds in solving the smile problem.

A newly creative empirical-distribution-based model (EDB model) which uses a histogram constructed from past asset prices has been applied to the S&P 500 index and it eliminates the degree of smile and the price difference. This study applies the same methodology on the TSM and UMC call warrants on the Taiwan stock market to compare its pricing and volatility smile with those derived from the Black-Scholes model. The results show that the degree of smile is not as great in the EDB model with a long historical horizon as in the BS model. Using the average value of the implied volatility as a standard deviation, the fitted prices were computed. The actual option price and both the fitted prices from the BS model and EDB model are all overpriced after examining the sell-naked profit. The profit from the EDB model is lower than the profit from the BS model and from the actual market price. This overpricing is more serious for the in-the-money than the out-of-the-money warrants and is less serious if longer historical data is used.