Power approximation for pricing American Options

Abstract

American options are one of the most traded instruments in the financial markets. However, pricing such options is challenging since there is the possibility of early exercise of the option. We propose a robust pricing method based on nonlinear regression over a large representative set of “exact” pricing instances obtained via a binomial lattice. Our nonlinear regression is sought to relate the price and the critical stock price of an American option to its key parameters via a power-type regression. Our “power approximation” approach is inspired from the operations research literature on the well-known (s, S) periodic review inventory system. Our objective is to develop a closed-form approximation for pricing American options that outperforms other existing approximations, in terms of accuracy and simplicity. Our results include developing a large set of near-exact American option prices over a carefully designed grid of parameter values that are common in practice. In addition, we compile the literature for existing American option pricing approximations, identify suitable ones, and apply the resulting approximations to the set of parameters in the test grid. These approximation serve two purposes, which we address in our work, (i) providing a starting point for our power approximations, and (ii) developing a benchmark to compare our algorithms against. In our work, we develop two closed-form approximations for the critical stock price and premium of an American put option, respectively. Both approximations are based on the Barone-Adesi & Whaley's results (1987). Correction factors fitted by regression are used to modify the results of Barone-Adesi & Whaley's (1987) to improve the accuracy. The two closed-approximations for the critical stock price and the premium of an American put option perform very well with a median relative absolute error of 0.3764% and 0.0795% respectively. As such, these approximations outperform their counterparts in the literature on both accuracy, computational efficiency (speed), and simplicity.