The valuation of put options with early-exercise opportunities constitutes a major challenge of asset pricing. The option-theoretic response to this challenge relies on the estimation of the optimal exercise boundary. This paper introduces a novel quadratic approximation for the valuation of American options on common stock. The paper’s contribution lies in the tradition of semi-analytical approximation of American put options, which was put forward in Barone-Adesi and Whaley (1987). Assuming that the interest rate and the volatility are constant, the early-exercise premium is modeled as a product of two functions, one being a function of time and the other being a function of the stock price. The numerical results demonstrate the accuracy of the method, over competing alternatives such as the Barone-Adesi and Whaley (1987) algorithm.

The analytical valuation of options with American-style exercise characteristics remains a pricing challenge for mathematicians and economists alike. This problem is particularly important since a majority of traded options are of the American type. Major pricing difficulties lie in the case of options on multiple assets. However, novel approximation approaches can provide important intuition, especially in the case of capital budgeting decisions in the real-options framework. In this paper, we propose a novel analytic approximation and our numerical results show that it is accurate for a wide range of parameter values.

Financial Risk Management Journal, Quadratic Approximation, Value of American Options, Valuation of American Call Options, Root Mean Square Error (RMSE).