Marco Avellaneda and Roberta Gamba

The calculation of price-sensitivities of contingent claims is formulated in the framework of Weighted Monte Carlo simulation. Rather than perturbing the parameters that drive the economic stata-variables of the model, we perturb the vector of probabilities of simulated paths in a neighborhood of the uniform distribution. The resulting hedge-ratios (sensitivities with respect to input prices) are characterized in terms of higher-order moments of simulated cash-flows. The computed sensitivities display excellent agreement with analytic closed-form solutions whenever the latter are available, e.g., with the Greeks of the Black-Scholes model, and with approximate analytic solutions for Basket Options in multi-asset models. The advantage of the new sensitivities is that they are ``universal'' and simple to compute: they do not require performing multiple MC simulations, discrete differentiation, or re-calibration of the simulation.