两资产亚式彩虹期权的定价研究

Study on two-asset Asian rainbow options pricing

研究一种奇异路径依赖型期权——两资产亚式彩虹期权的定价问题.基于Black-Scholes期权定价模型的假设条件,利用无套利原理,构建了反映两资产亚式彩虹期权路径依赖特征的多因素定价模型.并结合边界条件,推导了基于两个标的资产的几何亚式彩虹期权的解析定价公式,借助它运用蒙特卡罗模拟法中减少变量技术对两资产算术亚式彩虹期权定价,得到了该期权更精确的估计值.

This paper studies the pricing of a kind of exotic path-dependent options, i.e. two-asset Asian Rainbow options. On the basis of the hypotheses of the Black-Scholes option pricing model, using the arbitrage-free principle, we construct the multi-factors pricing model which corresponds to the path-dependent characteristic of Asian Rainbow options on two assets. With the boundary conditions, we derive the analytic pricing formula of the two-asset geometric Asian rainbow options. With the help of the above analytic solutions, we further use the variate reduction technique in the Monte Carlo simulation to evaluate the arithmetic Asian rainbow options with two-asset and obtain accurately simulated option price.