Numerical Pricing of Options under the Exponential Ornstein-Uhlenbeck Stochastic Volatility Model based on a DG Technique
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Date
2018
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Abstract
Stochastic volatility models are a variance extension of the classical Black-Scholes model dynamics by introducing another auxiliary processes to model the volatility of the underlying asset returns. Here we study the pricing problem for European-style options under a one-factor stochastic volatility model when the volatility of the underlying price is governed by the exponential Ornstein-Uhlenbeck process. The problem can be formulated as a non-stationary second-order degenerate partial differential equation accompanied by initial and boundary conditions, whose analytical solutions are not available in general. Therefore, the approximate option value is obtained by a numerical procedure based on a discontinuous Galerkin technique that provides promising results. Finally, reference numerical experiments are provided with the emphasis on the behaviour of the option values with respect to the discretization parameters.
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QUADRATIC SPLINE-WAVELETS