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Modern Stochastics: Theory and Applications


Option pricing in the model with stochastic volatility driven by Ornstein–Uhlenbeck process. Simulation
Volume 2, Issue 4 (2015), pp. 355–369
Pub. online: 17 December 2015      Type: Research Article      Open accessOpen Access
Received
2 December 2015
Revised
10 December 2015
Accepted
10 December 2015
Published
17 December 2015

Abstract

We consider a discrete-time approximation of paths of an Ornstein–Uhlenbeck process as a mean for estimation of a price of European call option in the model of financial market with stochastic volatility. The Euler–Maruyama approximation scheme is implemented. We determine the estimates for the option price for predetermined sets of parameters. The rate of convergence of the price and an average volatility when discretization intervals tighten are determined. Discretization precision is analyzed for the case where the exact value of the price can be derived.

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Copyright
© 2015 The Author(s). Published by VTeX
Open access article under the CC BY license.

Keywords
Financial markets stochastic volatility Ornstein–Uhlenbeck process option pricing discrete-time approximations Euler–Maruyama scheme

MSC2010
91B24 91B25 91G20

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