Based on empirical evidence of fast mean-reverting spikes, electricity spot prices are often modeled $X+Z^\beta$ as the sum of a continuous It\^o semimartingale $X$ and a mean-reverting compound Poisson process $Z_t^\beta = \int_0^t\int_{\R} xe^{-\beta(t-s)}\underline{p}(ds,dt)$ where $\underline{p}(ds,dt)$ is Poisson random measure with intensity $\lambda ds\otimes dt$. In a first part, we investigate the estimation of $(\lambda,\beta)$ from discrete observations and establish asymptotic efficiency in various asymptotic settings. In a second part, we discuss the use of our inference results for correcting the value of forward contracts on electricity markets in presence of spikes. We implement our method on real data in the French, German and Australian market over 2015 and 2016 and show in particular the effect of spike modelling on the valuation of certain strip options. In particular, we show that some out-of-the-money options have a significant value if we incorporate spikes in our modelling, while having a value close to $0$ otherwise.
Abstract. Inverse problems appear naturally in a broad range of applications. Numerical analysis and statistics have -often independently -developed methods for regularisation and inversion. The aim of this mini-workshop is to bring together these methods and to consider their use in applications, with a focus on mathematical finance.Mathematics Subject Classification (2000): 62Gxx, 65R32, 91Bxx.
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