Recursive Algorithms for Pricing Discrete Variance Options and Volatility Swaps Under Time-Changed Lèvy Processes

28 Pages Posted: 14 Jul 2014 Last revised: 7 Aug 2017

See all articles by Wendong Zheng

Wendong Zheng

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

Chi Yuen

Hong Kong University of Science & Technology (HKUST)

Yue Kuen Kwok

Hong Kong University of Science & Technology - Department of Mathematics

Date Written: October 25, 2015

Abstract

We propose robust numerical algorithms for pricing discrete variance options and volatility swaps under general time-changed Lèvy processes. Since analytic pricing formulas of these derivatives are not available, some of the earlier pricing methods use the quadratic variation approximation for the discrete realized variance. While this approximation works quite well for long-maturity options on discrete realized variance, numerical accuracy deteriorates for options with low frequency of monitoring and/or short maturity. To circumvent these shortcomings, we construct numerical algorithms that rely on the computation of the moment generating function of the discrete realized variance under the time-changed Lèvy models. We adopt the randomization of the Laplace transform of the discrete log return with a standard normal random variable and develop a recursive quadrature algorithm to compute the moment generating function of the discrete realized variance. Our pricing approach is rather computationally efficient when compared with the Monte Carlo simulation and works particularly well for discrete realized variance and volatility derivatives with low frequency of monitoring and/or short maturity. The pricing properties of various variance and volatility derivatives under various time-changed Lèvy processes and the Heston model are also investigated.

Keywords: variance swaps, volatility swaps, variance options, time-changed Lèvy processes, discrete sampling

JEL Classification: G12

Suggested Citation

Zheng, Wendong and Yuen, Chi and Kwok, Yue Kuen, Recursive Algorithms for Pricing Discrete Variance Options and Volatility Swaps Under Time-Changed Lèvy Processes (October 25, 2015). Available at SSRN: https://ssrn.com/abstract=2465742 or http://dx.doi.org/10.2139/ssrn.2465742

Wendong Zheng

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

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

Chi Yuen

Hong Kong University of Science & Technology (HKUST)

Clearwater Bay
Kowloon, 999999
Hong Kong

Yue Kuen Kwok (Contact Author)

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

Clearwater Bay
Kowloon, 999999
Hong Kong

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