This paper presents a new approximation formula for pricing discretely monitored average options and spread options in a local-stochastic volatility (LSV) model with jumps.
Particularly, our model includes local-volatility functions and jump components in both the
underlying asset price and its volatility processes. To the best of our knowledge, the proposed approximation is the first one which achieves analytic approximations for the average and spread option prices in this environment.
In numerical experiments, by employing several models we provide approximate prices for
average and calendar spread options on the WTI futures based on the parameters through
calibration to the listed (plain-vanilla) futures option prices, and compare those with the
CME settlement prices, which confirms the validity of the method.
Moreover, we show the LSV with jumps model is able to replicate consistently and precisely listed futures option, calendar spread option and average option prices with common parameters.