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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 classical Black-Scholes option pricing model assumes that the return on assets follows the Brownian motion, but the real financial market is still jumping and the yield has the characteristics of “peak thick tail”, “implied volatility” and so on, so Black- The Scholes model can not describe it completely, and the Lévy process is a semi-martingale model with left-hand and right-hand continuous jumps, which can describe the real financial market more accurately. Therefore, this paper assumes that the underlying asset obeys the exponential Lévy process and solves the European arithmetic average Asian option pricing formula. The Monte Carlo method and the moment matching variance reduction technique are used to simulate the data. The results show that the Lévy process has superiority in Asian option pricing Sex.