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European call option issued on a bond governed by a geometric or a fractional geometric Ornstein-Uhlenbeck process
Volume 1, Issue 1 (2014), pp. 95–108
Yu. Mishura   G. Rizhniak   V. Zubchenko  

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https://doi.org/10.15559/vmsta-2014.1.1.2
Pub. online: 27 June 2014      Type: Research Article      Open accessOpen Access

Received
5 March 2014
Revised
25 April 2014
Accepted
5 June 2014
Published
27 June 2014

Abstract

European call option issued on a bond governed by a modified geometric Ornstein-Uhlenbeck process, is investigated. Objective price of such option as a function of the mean and the variance of a geometric Ornstein-Uhlenbeck process is studied. It is proved that the “Ornstein-Uhlenbeck” market is arbitrage-free and complete. We obtain risk-neutral measure and calculate the fair price of a call option. We consider also the bond price, governed by a modified fractional geometric Ornstein-Uhlenbeck process with Hurst index $H\in (1/2,1)$. Limit behaviour of the variance of the process as $H\to 1/2$ and $H\to 1$ is studied, the monotonicity of the variance and the objective price of the option as a function of Hurst index is established.

References

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Keywords
Objective option price fair option price modified geometric Ornstein-Uhlenbeck process modified geometric fractional Ornstein-Uhlenbeck process

MSC2010
60H10 60G18 91B25

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