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Moment Methods for Exotic Volatility Derivatives

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  • Claudio Albanese
  • Adel Osseiran

Abstract

The latest generation of volatility derivatives goes beyond variance and volatility swaps and probes our ability to price realized variance and sojourn times along bridges for the underlying stock price process. In this paper, we give an operator algebraic treatment of this problem based on Dyson expansions and moment methods and discuss applications to exotic volatility derivatives. The methods are quite flexible and allow for a specification of the underlying process which is semi-parametric or even non-parametric, including state-dependent local volatility, jumps, stochastic volatility and regime switching. We find that volatility derivatives are particularly well suited to be treated with moment methods, whereby one extrapolates the distribution of the relevant path functionals on the basis of a few moments. We consider a number of exotics such as variance knockouts, conditional corridor variance swaps, gamma swaps and variance swaptions and give valuation formulas in detail.

Suggested Citation

  • Claudio Albanese & Adel Osseiran, 2007. "Moment Methods for Exotic Volatility Derivatives," Papers 0710.2991, arXiv.org.
  • Handle: RePEc:arx:papers:0710.2991
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    File URL: http://arxiv.org/pdf/0710.2991
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    1. Albanese, Claudio, 2006. "Operator Methods, Abelian Processes And Dynamic Conditioning," MPRA Paper 5246, University Library of Munich, Germany, revised 06 Nov 2007.
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    Cited by:

    1. Albanese, Claudio & Vidler, Alicia, 2008. "Dynamic Conditioning and Credit Correlation Baskets," MPRA Paper 8368, University Library of Munich, Germany, revised 21 Apr 2008.
    2. Albanese, Claudio, 2006. "Operator Methods, Abelian Processes And Dynamic Conditioning," MPRA Paper 5246, University Library of Munich, Germany, revised 06 Nov 2007.

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    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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