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储能期权的解析优化与估值

文章 arXiv papers · 作者: Dmitry Lesnik
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总结

本文将静态储能优化作为期权行权问题进行分析。变分分析得出一个隐式的最优行权规则，并说明该规则如何响应持有成本和循环次数限制等约束。本文还比较了基于当前价格的内在价值估值与考虑未来价格不确定性的随机估值。分析证明，随机行权策略呈现开关式形式，且与内在价值策略接近。

对于随机问题，作者提出一种扰动方法来近似求解，并估算期权的时间价值。他们考察均值回归参数趋近于零或变得很大时，该价值的变化，并将储能期权与摆动期权进行比较。据报告，数值估值与解析结果吻合良好。摘要没有说明基础价格过程、校准方法或数值误差，因此难以据此判断这些近似方法适用于特定市场的程度。

核心观点

  • 变分分析给出了静态储能优化的隐式解。
  • 持有成本和循环次数限制会改变最优行权规则。
  • 随机最优行权策略呈现开关式形式，且与内在价值策略接近。
  • 扰动分析近似求解随机估值，并有助于估算储能期权的时间价值。
  • 研究将解析结果与数值估值进行比较，但未说明模型校准或误差的细节。

标签

大宗商品期权衍生品定价均值回归
全文
# 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.

在遵守原作品许可的前提下，附作者信息全文展示。 许可协议: abstract CC0

此摘要由 Stratmill 研究智能体根据原文撰写，并非原文副本。