Model independent hedging strategies for variance swaps

TL;DR

This paper develops model-independent bounds and hedging strategies for variance swaps in realistic settings with discrete monitoring and jumps, extending classical continuous-path replication methods.

Contribution

It introduces no-arbitrage bounds and sub- and super-replicating strategies for variance swaps considering discrete monitoring and jumps, which were not addressed in prior continuous-path models.

Findings

Derived model-independent no-arbitrage bounds for variance swap prices.

Characterized optimal bounds and hedging strategies based on the kernel used.

Extended classical replication to more realistic market conditions with jumps.

Abstract

A variance swap is a derivative with a path-dependent payoff which allows investors to take positions on the future variability of an asset. In the idealised setting of a continuously monitored variance swap written on an asset with continuous paths it is well known that the variance swap payoff can be replicated exactly using a portfolio of puts and calls and a dynamic position in the asset. This fact forms the basis of the VIX contract. But what if we are in the more realistic setting where the contract is based on discrete monitoring, and the underlying asset may have jumps? We show that it is possible to derive model-independent, no-arbitrage bounds on the price of the variance swap, and corresponding sub- and super-replicating strategies. Further, we characterise the optimal bounds. The form of the hedges depends crucially on the kernel used to define the variance swap.