Albanese, Claudio and Osseiran, Adel (2007): Moment Methods for Exotic Volatility Derivatives.
Download (248Kb) | Preview
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.
|Item Type:||MPRA Paper|
|Original Title:||Moment Methods for Exotic Volatility Derivatives|
|Keywords:||volatility derivatives; operator methods; moment methods; conditional corridor variance swaps; variance knockout options|
|Subjects:||G - Financial Economics > G1 - General Financial Markets > G13 - Contingent Pricing; Futures Pricing|
|Depositing User:||Claudio Albanese|
|Date Deposited:||16. Oct 2007|
|Last Modified:||18. Feb 2013 04:55|
Albanese, C. (2006). Operator Methods, Abelian Processes and Dynamic Conditioning. preprint, available at www.level3finance.com. Carr, P. and D. Madan (1998). Towards a theory of volatility trading. Volatility, Risk Publications, ed. Jarrow, R. Carr, P. and K. Lewis (2004). Corridor variance swaps. Risk February, 67–72. Carr, P. and R. Lee (2007). Realized Volatility and Variance: Options via Swaps. Risk. Darling, D. A. and M. Kac (Mar., 1957). On occupation times for marko processes. Transactions of the American Mathematical Society 84, 444–458. Derman, E., K. Demeterfi, M. Kamal and J. Zou (1999). More Than You Ever Wanted to Know about Volatility Swaps. Journal of Derivatives. Dupire, B. (1992). Arbitrage Pricing with Stochastic Volatility. preprint, Socit Gnrale. Johnson, N.L. and S. Kotz (1942). Continuous multivariate distributions. John Wiley and Sons. J.P. Morgan Securities (2006). Conditional variance swaps, product note. Technical report. Moler, C. and C.V. Loan (2003). Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later. SIAM Review pp. 3–30. Rebonato, R. and M. Joshi (2001). A joint empirical and theoretical investigation of the modes of deformation of swaption matrices: implications for model choice. QUARC Working paper.