# Variance and volatility swaps in energy markets

## Anatoliy Swishchuk

#### Abstract

ABSTRACT

This paper focuses on the pricing of variance and volatility swaps in the energy market. An explicit variance swap formula and a closed-form volatility swap formula (using the Brockhaus-Long approximation) for energy assets with stochastic volatility are found. These formulas follow the continuous-time generalized autoregressive conditional heteroskedasticity (1,1) (GARCH(1,1)) model (meanreverting) or the Pilipovic one-factor model. A numerical example is presented for the AECO natural gas index.