Efficient price sensitivity estimation of financial derivatives by weak derivatives

摘要

The stochastic gradient estimation method of weak derivatives (WD) is presented with the aim of constructing efficient algorithms for the estimation of the "Greeks" of financial derivatives. The key idea is to replace the derivative of the probability measure of the underlying model by its WD. The WD method has the same advantageous property of the well-known score function method that the form of the Greek estimator does not depend on the details of the payoff function but only on the probability density of the underlying model. Simulation studies indicate that the WD estimator has significantly lower variance than the score function and finite difference estimator, however, the associated computational burden in certain cases may not be negligible.