A general framework for discretely sampled realized variance derivatives in stochastic volatility models with jumps

Zhenyu Cui, J. Lars Kirkby and Duy Nguyen

European Journal of Operational Research, 2017, vol. 262, issue 1, 381-400

Abstract: After the recent financial crisis, the market for volatility derivatives has expanded rapidly to meet the demand from investors, risk managers and speculators seeking diversification of the volatility risk. In this paper, we develop a novel and efficient transform-based method to price swaps and options related to discretely-sampled realized variance under a general class of stochastic volatility models with jumps. We utilize frame duality and density projection method combined with a novel continuous-time Markov chain (CTMC) weak approximation scheme of the underlying variance process. Contracts considered include discrete variance swaps, discrete variance options, and discrete volatility options. Models considered include several popular stochastic volatility models with a general jump size distribution: Heston, Scott, Hull–White, Stein–Stein, α-Hypergeometric, 3/2 and 4/2 models. Our framework encompasses and extends the current literature on discretely sampled volatility derivatives, and provides highly efficient and accurate valuation methods. Numerical experiments confirm our findings.

Keywords: Finance; Volatility derivatives; Regime-switching; Jump diffusion; Stochastic volatility (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (44)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:262:y:2017:i:1:p:381-400

DOI: 10.1016/j.ejor.2017.04.007

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