A Stochastic Volatility Model, Volatility Smile and Forecasting Volatility

Abstract:     
In this paper we propose a stochastic valuation model based on the Fourier transform for option price. This model can be used for the valuation of European options, characterized by two state variables: the price of the underlying asset and its volatility. We model the stochastic processes described by the two variables to obtain a partial derivatives equation whose solution is the price of the derivative. We propose a solution to this partial derivatives equation using the Fourier transform. We assume a non-zero correlation between the underlying asset price and its volatility and two sources of risk: return and volatility. We also propose a volatility smile function.

Number of Pages in PDF File: 27

Keywords: Option valuation, Stochastic volatility, Volatility Smile, Volatility forecasting

JEL Classification: G10, G12, G13

working papers series