| Summary: | 碩士 === 東吳大學 === 商用數學系 === 90 === In general, the delta method which employed first order Taylor’s expansion is used to approximate the relationship between derivatives and its underlying factors when the portfolio contain non-linear contract such as options. If the performance of delta method does not perform well enough, the second order Taylor’s expansion, called delta-gamma method, can be employed. There are two potential errors implied in the delta approximation and delta-gamma approximation. First, the error of distribution assumption will occur when the distribution of underlying is not a normal distribution. Second, the error will occur when option price calculated by delta approximation and delta-gamma approximation. In this paper we introduce the EGB2 distribution to describe the behavior of security return. The EGB2 distribution can directly characterize the leptokurtosis, fat tails and skewness of security return. Under the no arbitrage assumption, we employ the method of moment to estimate the parameters of EGB2 distribution through real market daily return. We also employ the GB2 option pricing formula, proposed by McDonald & Bookstaber (1991), to calculate the Value-at-Risk (VaR) of options for different methods.
In our empirical study, we select ten Taiwan warrant data during 1999 and 2001 and calculate their VaRs. Because the daily change rate of security return in Taiwan is limited within [-7%, 7%], the leptokurtosis of security return is not obvious. We find that the major factor affect the VaR of option is not option pricing model but the VaR of security when the security return is independently and identically distributed. Also, the analytical approach is better than delta method and delta-gamma method in the empirical results.
|
|---|
