Abstract

Moment swaps are essentially forward contracts on realized higher moments of log-returns of a specified underlying asset, which play an important role in protection against different kinds of market shocks, and variance, skewness, and kurtosis swaps are examples of moment swaps currently traded in markets. To facilitate market practitioners, this work provides a simple and easy-to-use pricing formula of moment swaps on discrete sampling under the Black-Scholes model with time-dependent parameters. The formula is investigated for validity and compared with the fair delivery prices of moment swaps. Furthermore, a closed-form formula for hedging moment swaps on futures is deduced. Finally, Monte Carlo simulations are performed to support the accuracy of the pricing formula and numerical examples are provided to check the sensitivity of the parameters and relationships of calculated prices between moment swaps.