Modelling of the derivatives pricing with multifactor volatility

Abstract

The pricing of options generated by diffusion processes, where diffusion depends on two groups of variables, was carried out. An algorithm for calculating the approximate price of derivatives and the accuracy of valuations has been developed, which allows to perform the analysis and to make precautionary to minimize the risk of derivatives pricing arising on the stock market. The method of finding the indicative price for a wide class of derivatives has been expanded. Using the spectral theory of self-adjoint operators in Hilbert space and the wave theory of singular and regular perturbations, an analytical formula of the approximate asset price was set, which was described by models with stochastic volatility dependent on l-fast variable and n-slow variable factors, l≥1,n≥1, l∈N,n∈N and on local variable.