Efficient Computation of Option Price Sensitivities for Options of American Style

under the risk-neutral measure. As usual rd denotes the domestic interest rate, rf the foreign interest rate, σ the volatility. The analysis we do is also applicable to equity options, but we take the foreign exchange market as Abstract: No front-office software can survive without providing derivatives of option prices with respect to underlying market or model parameters, the so called Greeks. If a closed form solution for an option exists, Greeks can be computed analytically and they are numerically stable. However, for American style options, there is no closed-form solution. The price is computed by binomial trees, finite difference methods or an analytic approximation. Taking derivatives of these prices leads to instable numerics or misleading results, specially for Greeks of higher order. We compare the computation of the Greeks in various pricing methods and conclude with the recommendation to use Leisen-Reimer trees.