Efficient numerical pricing of American call options using symmetry arguments

This paper demonstrates that it is possible to improve significantly on the estimated call prices obtained with the regression and simulation-based least-squares Monte Carlo method by using put-call symmetry. The results show that, for a large sample of options with characteristics of relevance in real-life applications, the symmetric method performs much better on average than the regular pricing method, is the best method for most of the options, never performs poorly and, as a result, is extremely efficient compared to the optimal, but unfeasible method that picks the method with the smallest Root Mean Squared Error (RMSE). A simple classification method is proposed that, by optimally selecting among estimates from the symmetric method with a reasonably small order used in the polynomial approximation, achieves a relative efficiency of more than 98% . The relative importance of using the symmetric method increases with option maturity and with asset volatility. Using the symmetric method to price, for example, real options, many of which are call options with long maturities on volatile assets, for example energy, could therefore improve the estimates significantly by decreasing their bias and RMSE by orders of magnitude.