Valuation of options under a constant elasticity of variance process and stochastic volatility

Abstract

In this paper, we price European call options under a constant elasticity of variance process for the asset price and stochastic volatility. In particular, we derive an analytic approximation formula in the form of asymptotic expansions, which is valid for European options with short times to expiry. Further, we examine the performance of our formula on a market sample of short-tenor crude oil call options (traded on the International Commodities Exchange) and find that the formula provides an excellent fit to market prices.