Fast Hilbert Transform Algorithms for Pricing Discrete Timer Options Under Stochastic Volatility Models

25 Pages Posted: 14 Jul 2014 Last revised: 27 Oct 2015

See all articles by Pingping Zeng

Pingping Zeng

Hong Kong University of Science & Technology (HKUST) - Department of Mathematics

Yue Kuen Kwok

Hong Kong University of Science & Technology - Department of Mathematics

Wendong Zheng

Hong Kong University of Science & Technology (HKUST) - Department of Mathematics

Date Written: July 12, 2015

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 efficient and accurate 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 volatility of variance, correlation coefficient between the asset price process and instantaneous variance process, sampling frequency, and variance budget.

Keywords: timer options, Hilbert transform, stochastic volatility models

JEL Classification: G12

Suggested Citation

Zeng, Pingping and Kwok, Yue Kuen and Zheng, Wendong, Fast Hilbert Transform Algorithms for Pricing Discrete Timer Options Under Stochastic Volatility Models (July 12, 2015). Available at SSRN: https://ssrn.com/abstract=2465747 or http://dx.doi.org/10.2139/ssrn.2465747

Pingping Zeng

Hong Kong University of Science & Technology (HKUST) - Department of Mathematics ( email )

Rm. 3461, Lift 25-26
Clear Water Bay
Kowloon
Hong Kong

Yue Kuen Kwok (Contact Author)

Hong Kong University of Science & Technology - Department of Mathematics ( email )

Clearwater Bay
Kowloon, 999999
Hong Kong

Wendong Zheng

Hong Kong University of Science & Technology (HKUST) - Department of Mathematics ( email )

Rm. 3461, Lift 25-26
Clear Water Bay
Kowloon
Hong Kong

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