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Pricing Volatility Swaps Under Heston's Stochastic Volatility Model with Regime Switching

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Author Info

  • Robert Elliott
  • Tak Kuen Siu
  • Leunglung Chan

Abstract

A model is developed for pricing volatility derivatives, such as variance swaps and volatility swaps under a continuous-time Markov-modulated version of the stochastic volatility (SV) model developed by Heston. In particular, it is supposed that the parameters of this version of Heston's SV model depend on the states of a continuous-time observable Markov chain process, which can be interpreted as the states of an observable macroeconomic factor. The market considered is incomplete in general, and hence, there is more than one equivalent martingale pricing measure. The regime switching Esscher transform used by Elliott et al. is adopted to determine a martingale pricing measure for the valuation of variance and volatility swaps in this incomplete market. Both probabilistic and partial differential equation (PDE) approaches are considered for the valuation of volatility derivatives.

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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

Volume (Year): 14 (2007)
Issue (Month): 1 ()
Pages: 41-62

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Handle: RePEc:taf:apmtfi:v:14:y:2007:i:1:p:41-62

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Related research

Keywords: Regime switching Esscher transform; Markov-modulated Heston's SV model; observable Markov chain process; volatility swaps; variance swaps; regime switching OU-process;

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Cited by:
  1. Zhengjun Jiang & Martijn Pistorius, 2008. "Optimal dividend distribution under Markov-regime switching," Papers 0812.4978, arXiv.org, revised Apr 2011.
  2. Marcos Escobar & Daniela Neykova & Rudi Zagst, 2014. "Portfolio Optimization in Affine Models with Markov Switching," Papers 1403.5247, arXiv.org.
  3. Qi-min, Zhang, 2011. "Convergence of numerical solutions for a class of stochastic age-dependent capital system with Markovian switching," Economic Modelling, Elsevier, vol. 28(3), pages 1195-1201, May.
  4. Siu, Tak Kuen, 2008. "A game theoretic approach to option valuation under Markovian regime-switching models," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1146-1158, June.
  5. Leunglung Chan & Eckhard Platen, 2010. "Exact Pricing and Hedging Formulas of Long Dated Variance Swaps under a $3/2$ Volatility Model," Papers 1007.2968, arXiv.org, revised Jan 2011.
  6. Lorenzo Torricelli, 2012. "Valuation of asset and volatility derivatives using decoupled time-changed L\'{e}vy processes," Papers 1210.5479, arXiv.org, revised Feb 2014.

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