An analytic expansion method for the valuation of double-barrier options under a stochastic volatility model

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• 作者：Junkee Jeon^a ; ^{hollman@snu.ac.kr} ; Ji-Hun Yoon^b ; ^{yssci99@pusan.ac.kr} ; Chang-Rae Park^c ; ^d
• 关键词：Double-barrier option ; Stochastic volatility ; Asymptotic analysis ; Mellin transform method
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 May 2017
• 年：2017
• 卷：449
• 期：1
• 页码：207-227
• 全文大小：677 K
• 卷排序：449

文摘

In this paper, we study a double-barrier option with a stochastic volatility model whose volatility is driven by a fast mean-reverting process, where the option's payoff is extinguished as the underlying asset crosses one of two barriers. By using an asymptotic analysis and Mellin transform techniques, we derive semi-analytic option pricing formulas with the sum of a leading-order term and a correction-order term, and then the accuracy of the first approximation price of the double-barrier option is verified by using Monte Carlo simulation. Moreover, we analyze the impact of stochastic volatility on the double-barrier option prices. Finally, we demonstrate that our results enhance the existing double-barrier option price structures in view of flexibility and applicability through the market price of volatility risk.