Fourier Transform Algorithms for Pricing and Hedging Discretely Sampled Exotic Variance Products and Volatility Derivatives under Additive Processes

Zheng, Wendong; Kwok, Yue Kuen

doi:10.2139/ssrn.2194936

Cited by 6 publications

(1 citation statement)

References 32 publications

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“…A review of the fast Fourier transform option pricing algorithms is presented by Kwok et al (2012). Applications of the Fourier transform pricing algorithms for various discrete exotic derivatives are quite numerous, like pricing of discrete barrier and American options (Jackson et al, 2008) and discrete variance options (Zheng and Kwok, 2013). In this paper, we apply the fast Hilbert transform algorithm for pricing discrete timer options under general stochastic volatility models.…”

Section: Introductionmentioning

confidence: 99%

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

Zeng

Kwok

Zheng

2015

Int. J. Theor. Appl. Finan.

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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.

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Section: Introductionmentioning

confidence: 99%