Moment Methods for Exotic Volatility Derivatives

Claudio Albanese and Adel Osseiran

MPRA Paper from University Library of Munich, Germany

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.

Keywords: volatility derivatives; operator methods; moment methods; conditional corridor variance swaps; variance knockout options (search for similar items in EconPapers)
JEL-codes: G13 (search for similar items in EconPapers)
Date: 2007-10-10
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Citations: View citations in EconPapers (2)

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Related works:
Working Paper: Moment Methods for Exotic Volatility Derivatives (2007)
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Persistent link: https://EconPapers.repec.org/RePEc:pra:mprapa:5330

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