FINTECH THRUST SEMINAR | Path Weighting Method for Spot Sensitivities

Path Weighting Method for Spot Sensitivities

Abstract:

This is an on-going project (joint with Michel Gauthier) on efficient Monte Carlo computation of spot sensitivies for financial derivatives. The widely used bump-and-revaluate approach is simple yet biased and time consuming (O(N) for the full Delta vector and O(N^2) for the full Gamma matrix). In contrast, the path weighting method (a.k.a. pathwise sensitivities) is unbiased and computational efficient (O(1) for both full Delta and full Gamma), however, it suffers from a short-time variance blow-up effect, which is the main reason why it is barely used in industry. In this work, we derive a variance reduced path weighting formula for general Markov stock dynamics, and establish error bounds under different regularity assumptions on the payoff. The variance reduced path weighting formula is again of O(1) time complexity for computation of full Delta and full Gamma, and the estimation variance is similar to or smaller than that produced by the bump-and-reevaluate approach.