Pricing Barrier Options with Square Root Process

The square root constant elasticity of variance (CEV) process has been paid little attention in previous research on valuation of barrier options. In this paper we derive analytical option pricing formulae of up-and-out options with this process using the eigenfunction expansion technique. We develop an efficient algorithm to compute the eigenvalues where the basis functions in the formulae are the confluent hypergeometric functions. The numerical results obtained from the formulae are compared with the corresponding model prices under the Black-Scholes model. We find that the differences in the model prices between the square root CEV model and the Black-Scholes model can be significant as the time to maturity and volatility increase.