Pricing methods and hedging strategies for volatility derivatives

Abstract

In this paper we investigate the behaviour and hedging of discretely observed volatility derivatives. We begin by comparing the effects of variations in the contract design, such as the differences between specifying log returns or actual returns, taking into consideration the impact of possible jumps in the underlying asset. We then focus on the difficulties associated with hedging these products. Naive delta-hedging strategies are ineffective for hedging volatility derivatives since they require very frequent rebalancing and have limited ability to protect the writer against possible jumps in the underlying asset. We investigate the performance of a hedging strategy for volatility swaps that establishes small, fixed positions in straddles and out-of-the-money strangles at each volatility observation.

A Closed-Form Exact Solution for Pricing Variance Swaps With Stochastic Volatility

“…By exploring a dimension reduction technique, their numerical approach achieves high efficiency and accuracy for discretely-sampled variance swaps. Windcliff et al (2006) also explored a numerical algorithm to evaluate discretely-sampled volatility derivatives using numerical partial-integro differential equation approach.…”

“…Although these two numerical methods evaluate vari-ance swaps based on discretely-sampled realized variance and achieve high accuracy, the major limitation is that their models do not incorporate stochastic volatilities that are the most commonly used to model the dynamics of equity indices. To remedy this drawback, Little and Pant (2001) and Windcliff et al (2006) pointed out, respectively, in the conclusions of their papers that for better pricing and hedging general variance swaps one needs to adopt an appropriate model that incorporates the stochastic volatility characteristics observed in financial markets.…”

Pricing variance swaps under stochastic volatility and stochastic interest rate

“…The main tool was the assumption of the local volatility as a known function of time and spot price of the underlying asset. Furthermore, Windcliff et al [109] investigated the effects of employing the partial-integro differential equation on constant volatility, local volatility and jump diffusion-based volatility products using delta-gamma hedging. Large transaction costs involved in constant volatility models may result in inefficiency of their delta-gamma hedging modus.…”

Fourier Transform Algorithms for Pricing and Hedging Discretely Sampled Exotic Variance Products and Volatility Derivatives under Additive Processes

“…Little and Pant (2001) propose a finite difference method for numerical valuation of discretely sampled variance swaps under the local volatility model. Windcliff et al (2006) develop robust numerical schemes that solve the partial integraldifferential option pricing equation under jump-diffusion asset price dynamics. The high level of path dependence in discretely sampled volatility derivatives is handled by tracking two stochastic state variables that capture the jump of the sampled variance across a monitoring date.…”