Analytical Optimization and Valuation of Energy Storage Options

Summary

The document analyzes static energy storage optimization as an option exercise problem. Variational analysis yields an implicit optimal exercise rule and shows how it responds to constraints such as carry costs and limits on cycling. It also compares intrinsic valuation, based on current prices, with stochastic valuation, which accounts for future price uncertainty. The analysis establishes that the stochastic exercise strategy has a bang-bang form and stays close to the intrinsic strategy.

For the stochastic problem, the authors develop a perturbation method to approximate the solution and estimate the option’s time value. They examine how that value behaves as the mean reversion parameter approaches zero or becomes large, and compare storage options with swing options. Numerical valuations are reported to agree well with the analytical results. The summary does not specify the underlying price process, calibration, or numerical error, so it gives limited information for assessing how well the approximations transfer to particular markets.

Key ideas

• Variational analysis gives an implicit solution to static storage optimization.
• Carry costs and cycling limits change the optimal exercise rule.
• The stochastic optimal exercise strategy has a bang-bang form and remains close to the intrinsic strategy.
• Perturbation analysis approximates stochastic value and helps estimate storage option time value.
• Analytical results are compared with numerical valuations, though the document gives no details on model calibration or error.

Tags

# Storage option an Analytic approach


# Storage option an Analytic approach









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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.