Currency option pricing with Wishart process

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:238

Article

Leung, Kwai Sun¹  Wong, Hoi Ying²  Ng, Hon Yip³ 

[1] Hong Kong Baptist Univ, Beijing Normal Univ, United Int Coll, Div Sci & Technol, Zhuhai 519085, Peoples R China

[2] Chinese Univ Hong Kong, Dept Stat, Shatin, Hong Kong, Peoples R China

[3] Chinese Univ Hong Kong, Dept Syst Engn & Engn Management, Shatin, Hong Kong, Peoples R China

关键词: Exchange rate;    Mean reversion;    Option pricing;    Stochastic skew;    Stochastic volatility;    Wishart process;   

DOI  :  10.1016/j.cam.2012.08.029

来源: Elsevier

【 摘 要 】

It has been well-documented that foreign exchange rates exhibit both mean reversion and stochastic volatility. In addition to these, recent empirical evidence shows a stochastic skew of implied volatility surface from currency option data, which means that the slope of implied volatility curve of a given maturity is stochastically time varying. This paper develops a currency option pricing model which accommodates for this phenomena. The proposed model postulates that the log-currency value follows a mean reverting process with stochastic volatility driven by Wishart process under risk-neutral measure. Pricing formula for European currency option is derived in terms of Fourier Transform. Benchmarking against the Monte Carlo simulation, our numerical examples reveal that the pricing formula is accurate and remarkably efficient. The proposed model is also generalized to include jumps. The ability of the our model on capturing stochastic skew is illustrated through a numerical example. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

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