Estimating fast mean-reverting jumps in electricity market models

Abstract

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.

Local polynomial estimation of the intensity of a doubly stochastic Poisson process with bandwidth selection procedure

“…We keep only the increments verifying ∆ i S∆ i+1 S < 0 as jumps with ∆ i S = S ti − S ti−1 . When the frequency of observations ∆ goes to 0 and when β is large enough, [15] proves that this filtering allows to detect with probability one every spikes under some asymptotic conditions. The data are segmented in periods of one year for the detection of the jumps in order to avoid too much change in the volatility.…”

“…Let us consider N the Poisson process associated to the jump times of X. N has intensity (λ t ) 0≤t≤T which is the intensity we want to estimate as a function of the temperature. In order to detect the jumps, we use the method of [15] with a threshold equal to 5σ∆ 0.49 where ∆ is the frequency of observations and σ is the multipower variation estimator of order 20. We keep only the increments verifying ∆ i S∆ i+1 S < 0 as jumps with ∆ i S = S ti − S ti−1 .…”

“…The data are segmented in periods of one year for the detection of the jumps in order to avoid too much change in the volatility. In [15], the intensity of the Poisson process is constant. Assuming that λ is bounded below and above, the results can easily be extended to the case where λ is stochastic.…”

A survey of electricity spot and futures price models for risk management applications

“…We can observe that this formula is similar to (5) with the addition of an extra term that depends on the parameters of the Poisson process. Thus, as in [110,168,170,79], this additional term has a weak effect on the long-maturity futures prices. This is consistent with the fact that the spikes are short-term events.…”

“…For example, Hambly et al [110] propose numerical methods for the calculation of European and swing options in the case of the model (18). Deschatre et al [79] study the estimation of the parameters of the model (18) in a more general case where X 1 is an Itô semi-martingale. The estimated values of the mean-reverting parameter α 2 are very strong, which is consistent with the time series aspect.…”