欧式算术平均亚式期权定价——基于Lévy过程的Monte Carlo仿真

Valuation of the European Arithmetic Average Asian Option——Monte Carlo Simulation Based on Lévy Process

经典的Black-Scholes期权定价模型假定资产收益率服从布朗运动,但现实中的金融市场存在跳跃且收益率具有"尖峰厚尾"、"隐含波动率"等特征,因此Black-Scholes模型不能对其进行完全描述,而Lévy过程是左极限右连续带跳的半鞅模型,更能准确地描述真实的金融市场。故本文假定标的资产服从指数Lévy过程,求解欧式算术平均亚式期权定价公式,利用Monte Carlo方法并结合矩匹配的方差减小技术对数据进行仿真,结果表明Lévy过程在亚式期权定价中具有优越性。

The Classic Black-Scholes option pricing model assumes that asset returns follow Brownian motion, but the jump phenomenon appears the reality of financial markets. Returns have fat tail and implied volatility characteristics. Black-Scholes model cannot completely describe the financial markets. Lévy process is semi-continuous martingale model with jump, and more accurately describes the real financial markets. Therefore, this paper assumes that the underlying asset follow exponential Lévy process. The pricing formulae for the European arithmetic average Asian option was obtained. Using Monte Carlo method combined with the variance reduction technique of moment matching to simulate the data, the superiority of Lévy process in Asian option pricing is indicated.