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Research Article Open access CC BY 4.0

On Stochastic Volatility in the Valuation of European Options

Chuma Raphael Nwozo, Sunday Emmanuel Fadugba

Journal of Advances in Mathematics and Computer Science · pp. 104–127 · Published 18 Oct 2014

10.9734/BJMCS/2015/13176

Abstract

This paper presents stochastic volatility in the valuation of European options. Stochastic volatility models treat the volatility of the underlying asset as a random process rather than the constant volatility assumption of the Black-Scholes model. By changing the model parameters, almost all kinds of asset distributions can be generated by a negative correlation between the stock price process and the volatility process. It is observed that an asset’s log-return distribution is non-Gaussian which is characterized by heavy tails and high peaks. Heston model presents a new approach for a closed form valuation of options specifying the dynamics of the squared volatility as a square-root process and applying Fourier inversion techniques for the pricing procedure. Determination of the market growth rate of the stock share was considered. We also considered the effect of volatility and correlation parameter on the kurtosis and skewness of the density function.

European option Heston model Nigerian stock exchange, stochastic volatility model.

References (16)

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Cited by 4

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Alternative Approach for the Solution of the Black-Scholes Partial Differential Equation for European Call Option

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Hybrid Equity Warrants Pricing Formulation under Stochastic Dynamics

Teh Raihana Nazirah Roslan, S. Z. Ibrahim, S. Karim · 2020

On the Combination of Merton and Heston Models in the Theory of Option Pricing

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