Pricing holder-extendable call options with mean-reverting stochastic volatility


  • Siti Nur Iqmal Ibrahim Universiti Putra Malaysia.
  • Adan Diaz-Hernandez Universidad Anahuac Mexico-Norte.
  • John G. O'Hara University of Essex.
  • Nick Constantinou Deceased



extendable options, Heston model, fast Fourier transform, finite difference method, Monte Carlo simulation.


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. doi:10.1017/S1446181119000142

Author Biographies

Siti Nur Iqmal Ibrahim, Universiti Putra Malaysia.

Department of Mathematics, Faculty of Science and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor, Malaysia.

Adan Diaz-Hernandez, Universidad Anahuac Mexico-Norte.

Faculty of Economics and Business, Universidad Anahuac Mexico-Norte, Huixquilucan 52786, Mexico.

John G. O'Hara, University of Essex.

School of Computer Science and Electronic Engineering, University of Essex, Colchester CO4 3SQ, UK.





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