Derivative Pricing: Predictive Analytics Methods and Models

Abstract

Abstract. The article deals with the study of pricing and calculating the volatility of European options with general local-stochastic volatility applying Taylor series methods for degenerate diffusion processes, in particular for diffusion with inertia. The application of this idea requires new approaches caused by degradation difficulties. Price approximation is obtained by solving the Cauchy problem of partial differential equations diffusion with inertia, and the volatility approximation is completely explicit, that is, it does not require special functions. If the payoff of options is a function of only x, then the Taylor series expansion does not depend on and an analytical expression of the fundamental solution is considerably simplified. We have applied an approach to the pricing of derivative securities on the basis of classical Taylor series expansion, when the stochastic process is described by the diffusion equation with inertia (degenerate parabolic equation). Thus, the approximate value of options can be calculated as effectively as the Black-Scholes pricing of derivative securities.