Some Advances in Markov Chain Bootstrapping of Continuous-Valued Stochastic Processes

Econometric analysis is continuously challenged by the new requirements emerging in different fields of research. Referring in particular to the area of finance and economics, numerical methods based on simulations are attempting to solve a wide range of problems (e.g. real and financial investment diversification, production optimization, pricing, hedging, etc.) of increasing complexity. A substantial help to these needs is coming from Markov chain bootstrapping, which is proving to be a powerful method to attack difficult simulation problems, where in particular the properties of a stochastic process can not be assessed clearly and trajectories show nonlinear dependences. In this paper, we expose some late advances in the research on Markov chain bootstrapping. In particular, we focus on the problem of adapting Markov chain theory (which is notoriously discrete-valued) to simulate continuous-valued stochastic processes in the sectors of electricity and environmental markets. As it is well known, the main processes governing these markets (i.e. prices and demand) can not be satisfactorily represented as geometric Brownian motions, as it is common for traditional financial markets. Indeed, nonlinearities are often recognized in the literature: spikes, stochastic volatility, seasonality, and switching regimes are typical features described in most econometric papers focusing on these markets. We apply our Markov chain bootstrapping and test its properties based on the time series of daily electricity prices observed on the German market.