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As market intermediaries, electricity retailers buy electricity from the wholesale market or self generate for re(sale) on the retail market. Electricity retailers are uncertain about how much electricity their residential customers will use at any time of the day until they actually turn switches on. While demand uncertainty is a common feature of all commodity markets, retailers generally rely on storage to manage demand uncertainty. On electricity markets, retailers are exposed to joint quantity and price risk on an hourly basis given the physical singularity of electricity as a commodity. In the literature on electricity markets, few articles deals on intra-day hedging portfolios to manage joint price and quantity risk whereas electricity markets are hourly markets. The contributions of the article are twofold. First, we define through a VaR and CVaR model optimal portfolios for specific hours (3am, 6am, . . . ,12pm) based on electricity market data from 2001 to 2011 for the French market. We prove that the optimal hedging strategy differs depending on the cluster hour. Secondly, we demonstrate the significantly superior efficiency of intra-day hedging portfolios over daily (therefore weekly and yearly) portfolios. 1clearly show that the losses of an optimal daily portfolio are at least nine times higher than the losses of optimal intra-day portfolios.

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For a large class of vanilla contingent claims, we establish an explicit Föllmer-Schweizer decomposition when the underlying is an exponential of an additive process. This allows to provide an efficient algorithm for solving the mean variance hedging problem. Applications to models derived from the electricity market are performed.

Abstract:The regime-switching Lévy model combines jump-diffusion under the form of a Lévy process, and Markov regime-switching where all parameters depend on the value of a continuous time Markov chain. We start by giving general stochastic results. Estimation is performed following a two-step procedure. The EM-algorithm is extended to this new class of jump-diffusion regime-switching models. Simulations are proposed, alongside an empirical application dedicated to the study of financial and commodity time series. When comparing the results with (i) non regime-switching models, and (ii) continuous regime-switching models (where the Lévy process is replaced by a classic Brownian motion), the Lévy regime-switching model outperforms other competitors.

We develop and implement a method for maximum likelihood estimation of a regime-switching stochastic volatility model. Our model uses a continuous time stochastic process for the stock dynamics with the instantaneous variance driven by a Cox-Ingersoll-Ross (CIR) process and each parameter modulated by a hidden Markov chain. We propose an extension of the EM algorithm through the Baum-Welch implementation to estimate our model and filter the hidden state of the Markov chain while using the VIX index to invert the latent volatility state. Using Monte Carlo simulations, we test the convergence of our algorithm and compare it with an approximate likelihood procedure where the volatility state is replaced by the VIX index. We found that our method is more accurate than the approximate procedure. Then, we apply Fourier methods to derive a semi-analytical expression of S&P 500 and VIX option prices, which we calibrate to market data. We show that the model is sufficiently rich to encapsulate important features of the joint dynamics of the stock and the volatility and to consistently fit option market prices.

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