Pricing holder-extendable call options with mean-reverting stochastic volatility
Options with extendable features have many applications in finance and these provide the motivation for this study. The pricing of extendable options when the underlying asset follows a geometric Brownian motion with constant volatility has appeared in the literature. In this paper, we consider hold...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Cambridge University Press
2015
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| Online Access: | http://psasir.upm.edu.my/id/eprint/46000/ http://psasir.upm.edu.my/id/eprint/46000/1/Pricing%20holder-extendable%20call%20options%20with%20mean-reverting%20stochastic%20volatility.pdf |
| Summary: | Options with extendable features have many applications in finance and these provide the motivation for this study. The pricing of extendable options when the underlying asset follows a geometric Brownian motion with constant volatility has appeared in the literature. In this paper, we consider holder-extendable call options when the underlying asset follows a mean-reverting stochastic volatility. The option price is expressed in integral forms which have known closed-form characteristic functions. We price these options using a fast Fourier transform, a finite difference method and Monte Carlo simulation, and we determine the efficiency and accuracy of the Fourier method in pricing holder-extendable call options for Heston parameters calibrated from the subprime crisis. We show that the fast Fourier transform reduces the computational time required to produce a range of holder-extendable call option prices by at least an order of magnitude. Numerical results also demonstrate that when the Heston correlation is negative, the Black–Scholes model under-prices in-the-money and over-prices out-of-the-money holder-extendable call options compared with the Heston model, which is analogous to the behaviour for vanilla calls. |
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