Moment Methods for Exotic Volatility Derivatives

TL;DR

This paper develops operator algebraic and moment-based methods for pricing complex exotic volatility derivatives, accommodating flexible underlying models including jumps, stochastic volatility, and regime switching.

Contribution

It introduces a flexible, operator algebraic framework using Dyson expansions and moments for exotic volatility derivatives, extending to semi-parametric and non-parametric models.

Findings

Moment methods effectively price exotic volatility derivatives.

The framework accommodates complex models like jumps and regime switching.

Explicit valuation formulas for various exotic derivatives are provided.

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.