Simple Analytical Formulas for Pricing and Hedging Moment Swaps

Kittisak Chumpong, Khamron Mekchay, Sanae Rujivan, Nopporn Thamrongrat

Abstract

Moment swaps are essentially forward contracts on realized highermoments of log-returns of a specied underlying asset, which play an importantrole in protection against dierent kinds of market shocks, and variance, skewness,and kurtosis swaps are examples of moment swaps currently traded in markets. Tofacilitate market practitioners, this work provides a simple and easy-to-use pricingformula of moment swaps on discrete sampling under the Black-Scholes modelwith time-dependent parameters. The formula is investigated for validity andcompared with the fair delivery prices of moment swaps. Furthermore, a closed-form formula for hedging moment swaps on futures is deduced. Finally, MonteCarlo simulations are performed to support the accuracy of the pricing formulaand numerical examples are provided to check the sensitivity of the parametersand relationships of calculated prices between moment swaps.