| | |
Summary: MOMENT METHODS FOR EXOTIC VOLATILITY
DERIVATIVES
CLAUDIO ALBANESE AND ADEL OSSEIRAN
Abstract. The latest generation of volatility derivatives goes beyond vari-
ance and volatility swaps and probes our ability to price realized variance and
sojourn times along bridges for the underlying stock price process. In this pa-
per, 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, in-
cluding 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.
1. Introduction
Volatility derivatives are designed to facilitate the trading of volatility, thus
allowing one to directly take a range of tailored views. A basic contract is the
|
