New proxy schemes for swing contracts

This paper considers the valuation of swing contracts for energy markets using semi-analytical proxies. Using accurate Monte Carlo or finite-difference methods is computationally expensive. Therefore, different approximations have been introduced in the literature: for example, Keppo’s method replicates the swing contract by forwards and call options. We develop Keppo’s method further by introducing two new schemes that build on this approach. Our first methodology adds the probability of exercising the option to the constraints. Our second approach, where the quantities depend on the actual spot level, goes one step further such that the constraints on the total amount are satisfied in a weak sense, which leads to an upper bound for the price. We perform several numerical experiments with a one-factor Lucia–Schwartz model to show the improved quality of the numerical results for different contract parameters. Both of our methods yield a more accurate calculated price than the commonly used approach while retaining its computational advantage.