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題名：Option Pricing with Higher Moments Consideration
作者：謝長杰
作者(外文)：Chang-Chieh Hsieh
校院名稱：東吳大學
系所名稱：經濟學系
指導教授：林忠機
學位類別：博士
出版日期：2014
主題關鍵詞：Edgeworth；Gram-Charlier；Saddlepoint；Skewness；Kurtosis
原始連結：連回原系統網址new window
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This dissertation consists of three essays, one of which examines if it is possible to find the characteristic that can be adapted to abnormal fluctuations and unpredictable cluster effects in the real world by refining the traditional covered-call strategy with stochastic volatility in order to improve this strategy under the Black and Scholes model (1973). Since the distribution of the return of the target asset in the real world is highly likely to be left-skewed and leptokurtic, it will influence the accuracy of the option pricing; otherwise, the basic hypothesis of the return of the target asset is normally distributed, such as in the simple BS model, the GARCH pricing model, and many other stochastic volatility models. Therefore, this study adopts three approximations to price - Gram-Charlier approximate solution, Edgeworth approximate solution, and Shaddlepoint approximate solution - in order to take skewness and kurtosis into account. The first two approximate solutions are derived from the Approximation of Taylor Series Expansion. The laster solution is derived from the asymptotics method from the concept in statistics.
Under the consideration of skewness and kurtosis in the pricing model of European options, this paper introduces three analytic solutions and their detailed derivations. First, this paper compares these three approximations with numerical simulations to show the possible bad effects mentioned by other scholars in the past literature. The bad effect entails out of the possible range between zero to one in the probability density function. Second, this paper compares the accuracy among these three approximations by the benchmark Merton jump model (1976). Third, because American option pricing does not possess a closed-form and is not easy to price, many scholars have evaluated the price of American options in many different ways. This paper presents most of the different American option pricing methods that have been introduced in the literature and looks to further improve the American option pricing model introduced by Kallast and Kivinukk (2003). This paper integrates the three approximations into Kim’s integral equations and evaluates their accuracy with Monte Carlo simulation.
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