A chaos expansion approach under hybrid volatility models

作者：Funahashi Hideharu^*

来源：Quantitative Finance, 2014, 14(11): 1923-1936.

DOI：10.1080/14697688.2013.872283

• Black-Scholes model
• Smile and skew
• Successive substitution
• Wiener-Ito chaos expansion
• Hermite polynomial
• Hybrid stochastic and local volatility model

In this paper, we propose an approximation method based on the Wiener-Ito chaos expansion for the pricing of European contingent claims. Our method is applicable to widely used option pricing models such as local volatility models, stochastic volatility models and their combinations. This method is useful in practice since the resulting approximation formula is not computationally expensive, hence it is suitable for calibration purposes. We will show through some numerical examples that our approximation remains quite good even for the long maturity and/or the high volatility cases, which is a desired feature. As an example, we propose a hybrid volatility model and apply our approximation formula to the JPY/USD currency option market obtaining very accurate results.

• 出版日期2014-11-2