Storage option an Analytic approach

TL;DR

This paper presents an analytical approach to optimize storage options using variational analysis, exploring the impact of constraints, stochastic vs. intrinsic solutions, and perturbation methods to estimate time value.

Contribution

It introduces a novel analytical framework for storage option optimization, including explicit solutions and perturbation analysis for stochastic problems.

Findings

Optimal exercise strategy is 'bang-bang' in stochastic models.

Approximate solutions effectively estimate storage option time value.

Analytical results align well with numerical valuations.

Abstract

The mathematical problem of the static storage optimisation 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 optimisation problem. The obtained approximate solution allows us to estimate the time value of the storage option. 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.