Jump Diffusion Models and Commodity Futures Pricing
A multi-factor jump-diffusion model under a martingale framework showing that price jumps affect commodity futures, not just options, with implications for risk management.
This research examines how price jumps affect the valuation of commodity futures and options. The study challenges conventional wisdom by demonstrating that jumps influence both futures contracts and options on futures — not just the options layer alone.
Modeling Approach
The authors employ a multi-factor jump-diffusion model under a martingale framework to derive pricing solutions for commodity futures and their associated options. This extends standard geometric Brownian motion models by adding a compound Poisson jump process to capture rare, severe market movements.
Key Finding
Traditional futures pricing approaches may underestimate the consequences of jump risk on commodity valuations. When jump intensity or jump size is material, ignoring the jump component produces systematic pricing errors in the futures market — a finding with direct implications for hedging strategies.
Risk Management Implications
These findings suggest that practitioners in commodity markets should account for jump risk more comprehensively than existing continuous-diffusion models indicate. The martingale framework provides the mathematical infrastructure needed to do so consistently.