Valuation of American Continuous-Installment Options Under the Constant Elasticity of Variance Model

This article prices American-style continuous-installment options in the constant elasticity of variance (CEV) diffusion model where the volatility is a function of the stock price. We derive the semi-closed form formulas for the American continuous-installment options using Kim’s integral representation method and then obtain the closed-form solutions by approximating the optimal exercise and stopping boundaries as step functions. We demonstrate the speed-accuracy of our approach for different parameters of the CEV model. Furthermore, the effects on both option price and the optimal boundaries are discussed and the causes of underestimating or overestimating the option prices are analyzed under the classical Black-Scholes-Merton model, in particular, for the case of elasticity coefficient with numerical examples.

Efficient Numerical Valuation of Continuous Installment Options

In this work we investigate the novel Kryzhnyi method for the numerical inverse Laplace transformation and apply it to the pricing problem of continuous installment options. We compare the results with the one obtained using other classical methods for the inverse Laplace transformation, like the Euler summation method or the Gaver-Stehfest method.