Mathematics and Statistics Vol. 10(3), pp. 549 - 553
DOI: 10.13189/ms.2022.100310
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Pricing of A European Call Option in Stochastic Volatility Models

Said Taoufiki *, Driss Gretete
Engineering Sciences Laboratory, National school of Applied Sciences ENSAK, University Ibn Tofail, Morocco


Volatility occupies a strategic place in the financial markets. In this context of crisis, and with the great movements of the markets, traders have been forced to turn to volatility trading for the potential gain it provides. The Black-Scholes formula for the value of a European option to purchase the underlying depends on a few parameters which are more or less easy to calculate, except for the realized volatility at maturity which makes a problem, because there is no single value, nor an established way to calculate it. In this article, we exploit the Martingale pricing method to find the expected present value of a given asset relative to a riskneutral probability measure. We consider a bond-stock market that evolves according to the dynamics of the Black-Scholes model, with a risk-free interest rate varying with time. Our methodology has effectively directed us towards interesting formulas that we have derived from the exact calculation, giving the present value of the volatility realized over a period of maturity for a European option in a stochastic volatility model.

Stochastic Model, Volatility, SABR Model, Pricing

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Said Taoufiki , Driss Gretete , "Pricing of A European Call Option in Stochastic Volatility Models," Mathematics and Statistics, Vol. 10, No. 3, pp. 549 - 553, 2022. DOI: 10.13189/ms.2022.100310.

(b). APA Format:
Said Taoufiki , Driss Gretete (2022). Pricing of A European Call Option in Stochastic Volatility Models. Mathematics and Statistics, 10(3), 549 - 553. DOI: 10.13189/ms.2022.100310.