Executive Director of the Center for Quantitative Risk Analysis
PhD in Applied Mathematics from the Moscow Institute of Electronics and Mathematics in 1990. Served as Director of Research for TXU Energy Trading; Director of Quantitative Analysis for Reliant Energy; Chief Science Officer and VP of R&D for Integrated Energy Services.
Published in: Journal of Engineering Mathematics
Publication year: 2004
A new approach to modeling spikes in power prices proposed earlier by the author is presented and further developed. In contrast to the standard approaches, power prices with spikes as a non-Markovian stochastic process are modeled that allows for modeling spikes directly as self-reversing jumps. It is shown how this approach can be used to value and hedge European contingent claims on power with spikes. It is also shown that the values of European contingent claims on power with spikes satisfy the Cauchy problem for a certain linear evolution equation. In this way, the values of European contingent claims on power with spikes can be represented in terms of the Green’s function for this Cauchy problem and the Green’s function itself can be interpreted in terms of the values of the Arrow-Debreu securities on power with spikes.
A new approach to modeling spikes in power prices proposed earlier by the author is presented and further developed. In contrast to the standard approaches, power prices with spikes as a non-Markovian stochastic process are modeled that allows for modeling spikes directly as self-reversing jumps. It is shown how this approach can be used to value and hedge European contingent claims on power with spikes. It is also shown that the values of European contingent claims on power with spikes satisfy the Cauchy problem for a certain linear evolution equation. In this way, the values of European contingent claims on power with spikes can be represented in terms of the Green’s function for this Cauchy problem and the Green’s function itself can be interpreted in terms of the values of the Arrow-Debreu securities on power with spikes.