臺灣博碩士論文加值系統

本篇論文目的為在Heston’s stochastic volatility 假設下，建立適當評價障礙選擇權的方法。本篇參考Jason Fink在2003年所提出的靜態複製法以及San-Lin Chung、Pai-Ta Shih和Wei-Che Tsai在2009年提出對DEK靜態複製法的修正方法，更進一步推廣並降低誤差。而後，討論此方法的適用性。

The purpose of this thesis is to construct an effective method to evaluate the value of barrier options under Heston’s stochastic volatility model. We refer to Fink’s static replication method (2003) and the modified DEK static replication approach provided by Chung, Shih and Tsai (2009), and try to modified the method to reduce the error. Then discuss the applicability of this method.

Content
Chinese Abstract I
Abstract II
致謝 III
Content Ⅳ
List of Figures Ⅴ
1. Introduction 1
2. The model setting and approach review 3
2.1 Generalized Static Hedge Under Stochastic Volatility 4
2.2 A modified static hedging Jason Fink’s static replication method (2003) approach for DEK method 9
2.3 The Modified Geske-Johnson Formulae 10
3.1 Implementing the modified Fink’s method 11
3.2 Combine modified Geske-Johnson formulae and Fink’s method 13
3.3 D-1 match , D-2 match and D-3 match 13
4 Numerical Analysis and discussions 17
5 Conclusion 18
6 Appendix 19
7 Bibliography 22

Black, F., &; Scholes, M (1973). The pricing of options and corporate liabilities. Journal of Political Economy, 81, 637-654.
Chung, S.L., Shih, P.T., &; Tsai, W.C. (2009). A modified static hedging method for continuous barrier options. Journal of Futures Markets, Vol. 30, No. 12, 1150-1166.
Chung, S.L., &; Shih, P.T. (2008). Static hedging and pricing American options. Journal of Banking &; Finance, 33, 2140-2149.
Derman, E., Ergener, D., &; Kani, I. (1995). Static options replication. Journal of Derivatives, 2, 78-95.
Fink, J. (2003). An examination of the effectiveness of static hedging in the presence of stochastic volatility. Journal of Futures Markets, 23, 859-890.
Heston, S. L. (1993). A closed form solution for options with stochastic volatility with applications to bond and currency options. Review of Financial Studies, 6, 327-343.
Kato, T., &; Takahashi, A., &; Yamada, T (2013). An asymptotic expansion formula for up-and-out barrier option price under stochastic volatility model. JSIAM letters, Vol. 5, 17-20.
Richardson Extrapolation Techniques for The Pricing of American-style Options 2005