Pricing bounds and approximations for discrete arithmetic Asian options under time-changed Lévy processes
研究了时间变换Lévy过程下离散算术亚式期权的定价边界与近似方法，通过扩展条件变量法推导出下界和上界，数值测试表明部分精确有界近似能给出高精度结果，适用于Heston等常见模型。
We derive efficient and accurate analytical pricing bounds and approximations for discrete arithmetic Asian options under time-changed Lévy processes. By extending the conditioning variable approach, we derive the lower bound on the Asian option price and construct an upper bound based on the sharp lower bound. We also consider the general partially exact and bounded (PEB) approximations, which include the sharp lower bound and partially conditional moment matching approximation as special cases. The PEB approximations are known to lie between a sharp lower bound and an upper bound. Our numerical tests show that the PEB approximations to discrete arithmetic Asian option prices can produce highly accurate approximations when compared to other approximation methods. Our proposed approximation methods can be readily applied to pricing Asian options under most common types of underlying asset price processes, like the Heston stochastic volatility model nested in the class of time-changed Lévy processes with the leverage effect.