Pricing Real Options under the CEV Diffusion

Much of the work on real options assumes that the underlying state variable follows a geometric Brownian motion with constant volatility. This paper uses a more general assumption for the state variable process which may better capture the empirical observations found in the financial economics literature. We use the so-called constant elasticity of variance (CEV) diffusion model where the volatility is a function of the underlying asset price and provide analytical solutions for perpetual American-style call and put options under the CEV diffusion. When the constant risk-free interest rate r is different from the dividend yield q, the perpetual American option price is based on an infinite series of terms involving confluent hypergeometric functions. For r = q, the computation of the perpetual American option formula involves the use of modified Bessel functions. We demonstrate the implications of the correct specification of the underlying state variable process for the valuation of real assets and show that a firm that uses the standard geometric Brownian motion assumption is exposed to significant errors of analysis which may lead to non-optimal investment and disinvestment decisions