虹式亚洲期权定价

Pricing of rainbow Asian options

研究了一种奇异路径依赖型期权——具有虹式特征的亚洲期权的定价问题.基于Black-Scholes模型的假设条件,利用多维ITO引理和无套利原理,构建了基于两个资产支付红利的虹式亚洲期权多因素路径依赖型期权定价模型,并结合边界条件,导出虹式几何平均亚洲看涨期权的解析定价公式以及虹式几何平均亚洲期权看涨-看跌平价关系式,以此为控制变量模拟计算虹式算术平均亚洲期权,数值实验表明虹式几何平均控制变量法有效地提高了蒙特卡罗模拟虹式算术平均亚洲期权定价的精确度.

This paper studies the pricing of a kind of exotic path-dependent options,i.e.,Asian options with feature based on rainbow.On the basis of the hypotheses of the Black-Scholes model,we construct the rainbow Asian options on two assets paying dividends with multi-factors path-dependent option pricing model using the multidimensional ITO lemma and the arbitrage-free principle.With the boundary conditions,we derive the analytic formula of the rainbow geometric average Asian call option and call-put parity relationship on rainbow geometric average Asian options.With the help of the above analytic fomulae as the control variate,we further simulate the rainbow arithmetic average Asian options.The numerical evidence is shown that rainbow geometric average control variable method effectively improves the accuracy on Monte Carlo simulation of rainbow arithmetic average Asian option pricing.