Pricing Asian Options with Stochastic Convenience Yield and Jumps
33 Pages Posted: 30 Jan 2020
Date Written: January 9, 2020
We price Asian options on commodity futures contracts in the presence of stochastic convenience yield and interest rates as well as jumps in the commodity spot price. We obtain a closed-form solution for the geometric average case without the presence of jumps, both for continuous and discrete averaging. This analytic result enables us to apply suitable control variates to price an 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 option prices change accordingly. We then consider a variation of the model through 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 leads to a significant variance reduction, even though a closed form solution for a geometric average Asian option in the presence of jumps is unavailable.
Keywords: Asian Options, Stochastic Convenience Yield, Jump Diffusion, Derivatives
JEL Classification: G13, G11, D52, C63
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