Pricing bounds and approximations for discrete arithmetic Asian options under time-changed Lévy processes

We derive efficient and accurate analytical pricing bounds and approximations for discrete arithmetic Asian options under time-changed Lévy processes. We extend the conditioning variable approach to derive the lower bound on the Asian option price and construct a sharp upper bound based on the lower bound. We also consider the general partially exact and bounded (PEB) approximations, which includes the lower bound and partially conditional moments 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, including the Heston stochastic volatility model that is nested in time-changed Lévy processes with leverage effect.