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Partial differential equation methods to price options in the energy market.

机译：能源市场中价格期权的偏微分方程方法。

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摘要

We develop partial differential equation methods with well-posed boundary conditions to price average strike options and swing options in the energy market. We use the energy method to develop boundary conditions that make a two space variable model of Asian options well-posed on a finite domain. To test the performance of well-posed boundary conditions, we price an average strike call. We also derive new boundary conditions for the average strike option from the put-call parity. Numerical results show that well-posed boundary conditions are working appropriately and solutions with new boundary conditions match the similarity solution significantly better than those provided in the existing literature.;To price swing options, we develop a finite element penalty method on a one factor mean reverting diffusion model. We use the energy method to find well-posed boundary conditions on a finite domain, derive formulas to estimate the size of the numerical domain, develop a priori error estimates for both Dirichlet boundary conditions and Neumann boundary conditions. We verify the results through numerical experiments. Since the optimal exercise price is unknown in advance, which makes the swing option valuation challenging, we use a penalty method to resolve the difficulty caused by the early exercise feature. Numerical results show that the finite element penalty method is thousands times faster than the Binomial tree method at the same level of accuracy. Furthermore, we price a multiple right swing option with different strike prices. We find that a jump discontinuity can occur in the initial condition of a swing right since the exercise of another swing right may force its optimal exercise region to shrink. We develop an algorithm to identify the optimal exercise boundary at each time level, which allows us to record the optimal exercise time. Numerical results are accurate to one cent comparing with the benchmark solutions computed by a Binomial tree method.;We extend applications to multiple right swing options with a waiting period restriction. A waiting period exists between two swing rights to be exercised successively, so we cannot exercise the latter right when we see an optimal exercise opportunity within the waiting period, but have to wait for the first optimal exercise opportunity after the waiting period. Therefore, we keep track of the optimal exercise time when pricing each swing right. We also verify an extreme case numerically. When the waiting time decreases, the value of M right swing option price increases to the value of M times an American option price as expected.
机译：我们开发了具有良好边界条件的偏微分方程方法，以针对能源市场中的平均价格行使期权和波动期权。我们使用能量方法来开发边界条件，从而使亚洲期权的两个空间变量模型在有限域上处于适当位置。为了测试良好定位的边界条件的性能，我们对平均罢工价进行定价。我们还从看涨期权平价推导了平均行使价的新边界条件。数值结果表明，适定的边界条件是合适的，并且具有新边界条件的解与相似解的匹配要比现有文献提供的要好得多。恢复扩散模型。我们使用能量方法在有限域上找到适当的边界条件，推导公式以估计数值域的大小，为Dirichlet边界条件和Neumann边界条件开发先验误差估计。我们通过数值实验验证了结果。由于最优行使价事先是未知的，这使得摆动期权的估值具有挑战性，因此我们使用惩罚方法来解决早期行使特征所带来的困难。数值结果表明，在相同精度下，有限元罚分方法比二叉树方法快数千倍。此外，我们为具有不同行使价的多个右摆期权定价。我们发现，在挥杆动作的初始状态下可能会出现跳跃不连续现象，因为行使另一个挥杆动作可能会迫使其最佳运动区域收缩。我们开发了一种算法来识别每个时间级别的最佳运动边界，从而使我们能够记录最佳运动时间。与通过二项式树法计算的基准解决方案相比，数值结果精确到1％。;我们将应用程序扩展到具有等待时间限制的多个右摆选项。在两个要连续行使的摇摆权之间存在一个等待期，因此，当我们在等待期内看到最佳行使机会时，我们就不能行使后一项权利，而必须在等待期之后等待第一个最佳行使机会。因此，当对每个挥杆权定价时，我们会跟踪最佳运动时间。我们还通过数字验证了极端情况。当等待时间减少时，M右摇摆期权价格的值将增加到M乘以美国期权价格的值。

著录项

  • 作者

    Yan, Jinhua.;

  • 作者单位

    The Florida State University.;

  • 授予单位 The Florida State University.;
  • 学科 Mathematics.
  • 学位 Ph.D.
  • 年度 2013
  • 页码 80 p.
  • 总页数 80
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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