Vibrato Monte Carlo sensitivities. - Giles, M (Oxford-Man Institute of Quantitative Finance, 2007)
We show how the benefits of the pathwise sensitivity approach to computing Monte Carlo Greeks can be extended to discontinuous payoff functions through a combination of the pathwise approach and the Likelihood Ratio Method. With a variance reduction modification, this results in an estimator which for timestep h has a variance which is O(h−1/2) for discontinuous payoffs and O(1) for continuous payoffs. Numerical results confirm the variance is much lower than the O(h−1) variance of the Likelihood Ratio Method, and the approach is also compatible with the use of adjoints to obtain multiple first order sensitivities at a fixed cost.