# A Proposal for Multi-asset Generalised Variance Swaps

## TL;DR

This paper introduces new multi-asset generalized variance swaps based on eigenvalues and trace of covariance matrices, priced under Markov-modulated volatility models, with practical implications for hedging in commodities.

## Contribution

It proposes novel multi-asset variance swaps using eigen-value and trace measures, with pricing methods under Markov-modulated volatility models, and demonstrates their application with numerical examples.

## Key findings

- Effective pricing of new variance swaps for multiple assets.
- Numerical examples with three stocks illustrate the approach.
- Implications for risk hedging in commodity markets.

## Abstract

This paper proposes swaps on two important new measures of generalized variance, namely the maximum eigen-value and trace of the covariance matrix of the assets involved. We price these generalized variance swaps for financial markets with Markov-modulated volatilities. We consider multiple assets in the portfolio for theoretical purpose and demonstrate our approach with numerical examples taking three stocks in the portfolio. The resultsobtained in this paper have important implications for the commodity sector where such swaps would be useful for hedging risk