大阪大学　数理・データ科学教育研究センター
Center for Mathematical Modeling and Data Science,Osaka University

Stochastic volatility effects on static hedging

Yong-Ki Ma (Department of Applied Mathematics, Kongju National University)

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4. Stochastic volatility effects on static hedging

大阪大学 数理・データ科学セミナー 金融・保険セミナーシリーズ 第71回

Stochastic volatility effects on static hedging

Yong-Ki Ma (Department of Applied Mathematics, Kongju National University)

Hedging exotic options in financial market is an important work for the issuing financial instruments because the risk may cause huge losses for the financial instruments. The hedging methods are classified into two categories: the dynamic hedging approach and the static hedging approach. Our research is the latter. The static hedging approach is to form a portfolio with fixed weights of vanilla options, with varying strikes and maturities, which requires no adjustment in the future. Derman, Ergener, and Kani (1995, DEK) presented a methodology to hedge statically a large class of barrier options when an infinite number of vanilla options are available. This methodology is to set up a portfolio of vanilla options which replicates the barrier option’s payoff as close as possible. However, the result of this approach is only valid in very special cases and the possible extension to more advanced models seems rather difficult. To overcome this weakness, we propose stochastic volatility model driven by a fast mean-reverting Ornstein-Uhlenbeck process and then apply our model to DEK method. Our numerical results indicate that our model improves performance of static hedging.