A New Smoothed Perturbation Analysis Estimation of Greeks for Financial Options with Discontinuous Payoffs
报告人： Yanchu Liu, Sun Yat-Sen University
时间：2016-03-31 14:00 ~ 15:00
地点：Room 217, Guanghua Building 2
Greeks (also known as sensitivities) estimation is playing an increasingly important role in financial risk management. Pathwise and likelihood ratio methods are two common ways to estimate Greeks in Monte Carlo (MC) literature. Both of them produce unbiased estimates. The pathwise method usually has a smaller variance than the LR method. But it requires the payoff functions to be Lipschitz continuous, and therefore generally rules out discontinuous payoffs and the second-order Greeks. This paper proposes a new smoothed perturbation analysis (SPA) method that can liberate the Lipschitz continuity requirement on the payoff functions. The new estimator can be computed directly without calculating any conditional expectation or requiring nested simulation, which differs from existing SPA estimators. Under some moderate conditions, we prove that the proposed SPA estimate is unbiased and therefore enjoys the conventional MC convergence rate. Numerical results illustrate the advantage of our method for Asian options and Barrier options under the Black-Scholes and Heston models, respectively.
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