Confined exponential approximations for the valuation of the American put option

Abstract

Based on the Geske and Johnson (1984) compound option approach, we propose an alternative analytic approximation for an American put option by generalising the solutions of the confined exponential distribution. We introduce a confined exponential extrapolation scheme, which extends the Geske-Johnson Richardson extrapolation method and the Ho. Stapleton, and Subrahmanyam ( 1994) exponential extrapolation method. Establishing a specific restriction on the upper bound between the American put price and the number of exercise points provides a new insight into the compound option approach. Numerical results show that our new method not only overcomes the deficiencies in existing two-point extrapolation methods for long-term options but also fu1ther improves pric ing accuracy for short-term options, which may substitute adequately for numerical solutions. Comparative statistics with other existing analytic approximations are a lso presented.