A Stochastic Volatility Model, Volatility Smile and Forecasting Volatility

27 Pages Posted: 20 Jul 2004

See all articles by Bogdan Negrea

Bogdan Negrea

National Center for Scientific Research (CNRS)

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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.

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

JEL Classification: G10, G12, G13

Suggested Citation

Negrea, Bogdan, A Stochastic Volatility Model, Volatility Smile and Forecasting Volatility. Available at SSRN: https://ssrn.com/abstract=555709 or http://dx.doi.org/10.2139/ssrn.555709

Bogdan Negrea (Contact Author)

National Center for Scientific Research (CNRS) ( email )

3, rue Michel-Ange
Paris cedex 16, 75794
France

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