Nonlinear Sciences – Chaotic Dynamics
Scientific paper
2010-11-04
Nonlinear Sciences
Chaotic Dynamics
Conference Energy Finance / INREC 2010, Oct. 2010, Essen, Germany. 37 pages
Scientific paper
The mathematical problem of the static storage optimization is formulated and solved by means of a variational analysis. The solution obtained in implicit form is shedding light on the most important features of the optimal exercise strategy. We show how the solution depends on different constraint types including carry cost and cycling constraint. We investigate the relation between intrinsic and stochastic solutions. In particular we give another proof that the stochastic problem has a "bang-bang" optimal exercise strategy. We also show why the optimal stochastic exercise decision is always close to the intrinsic one. In the second half we develop a perturbation analysis to solve the stochastic optimization problem. The obtained approximate solution allows us to estimate the time value, which arises due to the stochastic nature of the price process. In particular we find an answer to rather academic question of asymptotic time value for the mean reversion parameter approaching zero or infinity. We also investigate the differences between swing and storage problems. The analytical results are compared with numerical valuations and found to be in a good agreement.
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