Pricing Options on Forwards in Energy Markets: The Role of Mean Reversion's Speed

Abstract

Consider the problem of pricing options on forwards in energy markets, when spot prices follow a geometric multi-factor model in which several rates of mean reversion appear. In this paper we investigate the role played by slow mean reversion when pricing and hedging options. In particular, we determine both upper and lower bounds for the error one makes neglecting low rates of mean reversion in the spot price dynamics.Keywords: electricity spot prices, multi-scale mean reversion, delivery period, options on forwards, hedging, pricing error, upper and lower bounds.

The Effect of Mean-Reverting Processes in the Pricing of Options in the Energy Market: An Arithmetic Approach

“…The main difference between Benth and Schmeck (2014) and Schmeck (2016) and our paper lie in the structure of the dynamics of the spot price process. These are geometric in Schmeck (2016), while arithmetic in this work. The choice of considering an arithmetic model has essentially two main reasons.…”

“…On the other hand, the drifted Brownian motion X simulates the randomly fluctuating long-term trend of the spot price, while the mean-reverting processes take care of the observed mean-reverting jump-component of the spot price. Notice that, differently to Schmeck (2016), among others, in our specification the price process can become negative due to the arithmetic structure of the considered dynamics. This is in line with the observation of negative prices of electricity.…”

“…We shall also assume that at the initial time t the swap price is observed, and it is equal for both models with |L| or |J| mean-reverting components; that is, F L (t, T 1 , T 2 ) = F J (t, T 1 , T 2 ) = F(t, T 1 , T 2 ). Moreover, following Schmeck (2016), we require that δ := F(t, T 1 , T 2 ) − K is constant, meaning that K = K(T 1 , T 2 ) has to be chosen accordingly in a delivery-period-dependent form. This condition enforces that call options with different delivery periods are comparable.…”

“…Our study is related to the one performed in Benth and Schmeck (2014) and Schmeck (2016) (see also Nomikos and Soldatos (2010) for a study of the importance of mean reversion and spikes in the stochastic behavior of the underlying asset when pricing options on power). The main difference between Benth and Schmeck (2014) and Schmeck (2016) and our paper lie in the structure of the dynamics of the spot price process. These are geometric in Schmeck (2016), while arithmetic in this work.…”

“…Second of all, using arithmetic models one can obtain explicit closed form formulas for the price of the swap price, given by the time-average of the spot price over the delivery period. This is not possible for geometric models, such that Benth and Schmeck (2014) and Schmeck (2016) approximate the delivery period by its midpoint.…”