Control Variates for Monte Carlo-Pricing of Three-Asset Spread Options with Application in the Energy Markets

Abstract: The purpose of this paper is to compare a collection of control variates for Monte Carlo-valuation of spread options on three assets with a view towards energy markets and to lay a foundation for continued research on control variates, e.g. combinations of control variates and adaption for quasi-Monte Carlo. The paper builds upon previous research on option pricing using Monte Carlo-simulation and closed form approximations. The use of underlying assets, underlying spread, call option, exchange options and delta hedge as control variates are tested in both a parametric study to test the impact of every input parameter, and a real-world scenario using data from the Dutch energy markets. In the real-world scenario the exchange option outperforms the other control variates in most cases. Uneven results for the exchange option in the parametric study leads to the conclusion that the use of delta hedge as control variate is the best performing based on the test results.