Storage option an Analytic approach
AbstractThe 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.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 1011.1234.
Date of creation: Nov 2010
Date of revision: May 2012
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Web page: http://arxiv.org/
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-11-13 (All new papers)
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