FAST HILBERT TRANSFORM ALGORITHMS FOR PRICING DISCRETE TIMER OPTIONS UNDER STOCHASTIC VOLATILITY MODELS

Pingping Zeng (), Yue Kuen Kwok and Wendong Zheng ()
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Pingping Zeng: Department of Mathematics, University of Vienna, Austria
Yue Kuen Kwok: Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong
Wendong Zheng: Hong Kong University of Science and Technology, Hong Kong

International Journal of Theoretical and Applied Finance (IJTAF), 2015, vol. 18, issue 07, 1-26

Abstract: Timer options are barrier style options in the volatility space. A typical timer option is similar to its European vanilla counterpart, except with uncertain expiration date. The finite-maturity timer option expires either when the accumulated realized variance of the underlying asset has reached a pre-specified level or on the mandated expiration date, whichever comes earlier. The challenge in the pricing procedure is the incorporation of the barrier feature in terms of the accumulated realized variance instead of the usual knock-out feature of hitting a barrier by the underlying asset price. We construct the fast Hilbert transform algorithms for pricing finite-maturity discrete timer options under different types of stochastic volatility processes. The stochastic volatility processes nest some popular stochastic volatility models, like the Heston model and 3/2 stochastic volatility model. The barrier feature associated with the accumulated realized variance can be incorporated effectively into the fast Hilbert transform procedure with the computational convenience of avoiding the nuisance of recovering the option values in the real domain at each monitoring time instant in order to check for the expiry condition. Our numerical tests demonstrate high level of accuracy of the fast Hilbert transform algorithms. We also explore the pricing properties of the timer options with respect to various parameters, like the volatility of variance, correlation coefficient between the asset price process and instantaneous variance process, sampling frequency, and variance budget.

Keywords: Finite-maturity timer options; Hilbert transform; stochastic volatility models (search for similar items in EconPapers)
Date: 2015
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Citations: View citations in EconPapers (3)

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DOI: 10.1142/S0219024915500466

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