Seasonality is an important topic in electricity markets, as both supply and demand are dependent on the time of the year. Clearly, the level of prices shows a seasonal behaviour, but not only this. Also, the price fluctuations are typically seasonal. In this paper, we study empirically the implied volatility of options on electricity futures, investigate whether seasonality is present and we aim at quantifying its structure. Although typically futures prices can be well described through multi-factor models including exponentially decreasing components, we do not find evidence of exponential behaviour in our data set. Generally, a simple linear shape reflects the squared volatilities very well as a curve depending on the time to maturity. Moreover, we find that the level of volatility exhibits clear seasonal patterns that depend on the delivery month of the futures. Furthermore, in an out-of-sample analysis we compare the performance of several implementations of seasonality in the one-factor framework.

In this paper, we consider a company that wishes to determine the optimal reinsurance strategy minimising the total expected discounted amount of capital injections needed to prevent the ruin. The company’s surplus process is assumed to follow a Brownian motion with drift, and the reinsurance price is modelled by a continuous-time Markov chain with two states. The presence of regime-switching substantially complicates the optimal reinsurance problem, as the surplus-independent strategies turn out to be suboptimal. We develop a recursive approach that allows to represent a solution to the corresponding Hamilton–Jacobi–Bellman (HJB) equation and the corresponding reinsurance strategy as the unique limits of the sequence of solutions to ordinary differential equations and their first- and second-order derivatives. Via Ito’s formula, we prove the constructed function to be the value function. Two examples illustrate the recursive procedure along with a numerical approach yielding the direct solution to the HJB equation.

In this paper we study the effect that mean-reverting components in the arithmetic dynamics of electricity spot price have on the price of a call option on a swap. Our model allows for seasonal effects, spikes, and negative values of the price of electricity. We show that for sufficiently large delivery periods of the swap contract, the error that one makes by neglecting some of the mean-reverting processes affecting the spot price evolution converges to zero. The decay rate is explicitly calculated. This is achieved by exploiting the additive structure of the electricity price process in order to determine an explicit closed-form formula for the price of the call on a swap. The theoretical analysis is then illustrated via a numerical example.