Pricing Average and Spread Options Under Local-Stochastic Volatility Jump-Diffusion Models

This paper presents a new approximation formula for pricing multidimensional discretely monitored average options in a local-stochastic volatility (LSV) model with jump by applying an asymptotic expansion technique. Moreover, it provides a justification of the approximation method with some asymptotic error estimates for general payoff functions. Particularly, our model includes local volatility functions and jump components in the underlying asset price as well as its volatility processes. To the best of our knowledge, the proposed approximation is the first one that achieves analytic approximations for the average option prices in this environment. In numerical experiments, by employing several models, we provide approximate prices for the listed average and calendar spread options on the West Texas Intermediate (WTI) futures based on the parameters through calibration to the listed (plain-vanilla) futures options prices. Then, we compare those with the Chicago Mercantile Exchange (CME) settlement prices, which confirms the validity of the method. Moreover, we show that the LSV with jump model is able to replicate consistently and precisely listed futures option, calendar spread option, and average option prices with common parameters.