Algorithmic Differentiation for Discontinuous Payoffs

We present a general technique to compute the sensitivities of the Monte Carlo price of discontinuous financial products. It is a natural extension of the pathwise adjoints method, which would require an almost-surely differentiable payoff; the efficiency of the latter method when many sensitivities must be calculated is preserved. We show empirically that the new algorithm is competitive in terms of accuracy and execution time when compared to benchmarks obtained by smoothing of the payoff, which benchmarks are biased and require a non-obvious tuning of their parameters.