Numerical Methods In Sensitivities Estimation Of Arithmetic Average Asian Option

As a kind of exotic options,Asian option with the payoff depends on the average of the underlying asset prices during a period is usually used to reduce the risks of market power.Options sensitivities reflect the risk characteristics of the options and play an important role in the development of trading strategies,risk management and other financial activities.Under the Black-Schole model,we are unable to obtain the analytical expression of the option price,thus the sensitivities could only be solved by numerical methods.In this paper,two methods,Pathwise and Likelihood,are used to solve the Delta,rho,Theta,vega and Gamma of arithmetic average Asian option.They convert these to integral problems and give unbiased estimators.We deduce the target functions under both methods and calculate them with Monte Carlo(MC)simulation and Quasi-Monte Carlo(QMC)simulation.Path generation method is the key of QMC simulation.We apply three general path generation methods,Random Walk,Brownian Bridge construction and Principal Component Analysis,and an Orthogonal Transform method for derivatives with discontinuous payoff to simulate,and analyze the impact on QMC efficiency.At the same time,we combine the Variance Reduction Techniques and QMC simulation for the Likelihood estimation.Taking geometric average Asian option as the control variable,the accuracy of the estimation of arithmetic average Asian option sensitivity has been improved significantly.