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Variance Swaps on Defaultable Assets and Market Implied Time-Changes

Author

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  • Matthew Lorig
  • Oriol Lozano Carbasse
  • Rafael Mendoza-Arriaga

Abstract

We compute the value of a variance swap when the underlying is modeled as a Markov process time changed by a L\'{e}vy subordinator. In this framework, the underlying may exhibit jumps with a state-dependent L\'{e}vy measure, local stochastic volatility and have a local stochastic default intensity. Moreover, the L\'{e}vy subordinator that drives the underlying can be obtained directly by observing European call/put prices. To illustrate our general framework, we provide an explicit formula for the value of a variance swap when the underlying is modeled as (i) a L\'evy subordinated geometric Brownian motion with default and (ii) a L\'evy subordinated Jump-to-default CEV process (see \citet{carr-linetsky-1}). {In the latter example, we extend} the results of \cite{mendoza-carr-linetsky-1}, by allowing for joint valuation of credit and equity derivatives as well as variance swaps.

Suggested Citation

  • Matthew Lorig & Oriol Lozano Carbasse & Rafael Mendoza-Arriaga, 2012. "Variance Swaps on Defaultable Assets and Market Implied Time-Changes," Papers 1209.0697, arXiv.org, revised Jul 2013.
    • Handle: RePEc:arx:papers:1209.0697
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    Cited by:

    1. Jing Li & Lingfei Li & Rafael Mendoza-Arriaga, 2016. "Additive subordination and its applications in finance," Finance and Stochastics, Springer, vol. 20(3), pages 589-634, July.
    2. Stefano De Marco & Caroline Hillairet & Antoine Jacquier, 2017. "Shapes of implied volatility with positive mass at zero," Working Papers 2017-77, Center for Research in Economics and Statistics.
    3. Stefano De Marco & Caroline Hillairet & Antoine Jacquier, 2013. "Shapes of implied volatility with positive mass at zero," Papers 1310.1020, arXiv.org, revised May 2017.
    4. Rafael Mendoza-Arriaga & Vadim Linetsky, 2014. "Time-changed CIR default intensities with two-sided mean-reverting jumps," Papers 1403.5402, arXiv.org.

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