Pricing Asian Options with Stochastic Convenience Yield and Jumps

Abstract

We price Asian options on commodity futures contracts in the presence of stochastic convenience yield, stochastic interest rates and jumps in the commodity spot price. We obtain a closed-form solution for the case of a geometric average option without the presence of jumps, both for continuous and discrete averaging. This analytic result enables us to employ the geometric average option as suitable control variate for pricing the corresponding arithmetic average Asian option via Monte Carlo simulation. We observe a significant reduction in the size of confidence intervals in relation to plain Monte Carlo. Varying the parameters of the model, we obtain a good understanding as to how Asian option prices change accordingly in relation to a stochastic convenience yield. We then consider a variation of the model by adding stochastic jumps to the commodity spot price dynamics. By conditioning on the jump times first and then averaging over the sequences of jump times, we show that our control variate still provides a significant variance reduction, even though a closed-form solution for a geometric average Asian option in the presence of jumps is unavailable.