Finite maturity caps and floors on continuous flows under the constant elasticity of variance process

Abstract

This paper offers novel analytical solutions for evaluating perpetual caps and floors on continuous flows under the constant elasticity of variance (CEV) model. We demonstrate that the inclusion of a perpetual bubble value is required to avoid arbitrage opportunities in the case of the CEV process with upward-sloping volatility skews. We then extend the previous literature on caps and floors arrangements by providing new analytical formulae for valuing finite maturity caps and floors that are contingent on continuous flows. We discuss the impact of the finite-lived solutions on the optimal behavior of a firm, relative to the perpetual case. We also show the implications of the correct specification of the underlying state variable process for the valuation of caps and floors by comparing the CEV results with the ones obtained when assuming a lognormal diffusion. Practical applications of these contractual agreements arising within the context of executive management decisions are also discussed.