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

Asymptotic Expansion Applied for Pricing Hybrid FX Option with Libor Market Models under the Stochastic Volatility and Heston Model in Currency Processes

長谷川貴博 （京都大学大学院 経営管理教育部）

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4. Asymptotic Expansion Applied for Pricing Hybrid FX Option with Libor Market Models under the Stochastic Volatility and Heston Model in Currency Processes

大阪大学 金融・保険セミナーシリーズ 第38回(CSFI-CRESTジョイントセミナー)

Asymptotic Expansion Applied for Pricing Hybrid FX Option with Libor Market Models under the Stochastic Volatility and Heston Model in Currency Processes

長谷川貴博 （京都大学大学院 経営管理教育部）

In this presentation, we will give a discourse on pricing Hybrid FX option between Libor Market Model under Stochastic Volatility and Heston Model in Currency Processes by means of an Asymptotic Expansion Method.

In many financial institutions, it is recommended that most of officers at market departments should adopt ideas of Libor Market Model in order to price interest rate derivatives (such as Cap/Floor, Swaption and so on) and it is natural that ideas of Libor Market Model be applied to discounting various assets described as stochastic differential equations.

In Monte Carlo Simulation, a frequently-used Simulation used in many financial institutions, however, pricing options with hybrid model requires much time and is just not realistic by using standard applications such as Excel etc. Hence other methods than Monte Carlo Simulation are required to reduce the burden for PCs and yet to produce the same effects. With an Asymptotic Expansion, an approximate probability density function can be obtained faster than with Monte Carlo Simulation and can be computed easily even with Excel only if every term of an Asymptotic Expansion is calculated.

In this research, it is confirmed whether pricing hybrid FX option between Libor Market Model and Heston Model with the use of an Asymptotic Expansion Method under the freezing method produces the same effect as Monte Carlo Simulation.