Application of the Esscher Transform to Pricing Forward Contracts on Energy Markets in a Fuzzy Environment

Abstract

The paper is dedicated to modeling electricity spot prices and pricing forward contracts on energy markets. The underlying dynamics of electricity spot prices is governed by a stochastic mean reverting diffusion with jumps having mixed-exponential distribution. Application of financial mathematics and stochastic methods enabled the derivation of the analytical formula for the forward contract’s price in a crisp case. Since the model parameters’ incertitude is considered, their fuzzy counterparts are introduced. Utilization of fuzzy arithmetic enabled deriving an analytical expression for the futures price and proposing a modified method for decision-making under uncertainty. Finally, numerical examples are analyzed to illustrate our pricing approach and the proposed financial decision-making method.

Keywords

• energy markets
• fuzzy sets
• stochastic processes
• jump-diffusion
• derivatives pricing
• decision making