Maren Schmeck: Electricity price modeling with stochastic time change

Electricity prices from liberalized electricity markets exhibit
characteristic features that are not observed in other commodity
markets. Besides strong seasonalities, electricity exhibits large price
spikes, which arise due to non-storability of electricity. The
occurrence and severity of such spikes are related to power generating
plant outages, but also depend strongly on the demand, which increases
dramatically during periods of abnormally high or low temperatures.
Moreover, price volatility is also related to demand, being higher
during periods of high demand, leading to seasonal patterns in
volatility. These features make electricity price modeling a challenging
task.

The powerful technique of stochastic time change allows to incorporate
stochastic as well as deterministic (e.g., seasonal) features in
stochastic process’ volatility. By specifying the base process as a mean
reverting jump diffusion and the time change as an absolutely continuous
stochastic process with seasonal component, we are able to
simultaneously model seasonal and stochastic effect in volatility and
jump components of the electricity price. We use temperature time series
as a proxy for the stochastic time change and show that this choice
leads to realistic price paths. We discuss model calibration and its
applications in Monte Carlo price simulations and risk management.