英文标题：
《Dirac Processes and Default Risk》
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作者：
Chris Kenyon and Andrew Green
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最新提交年份：
2015
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英文摘要：
We introduce Dirac processes, using Dirac delta functions, for short-rate-type pricing of financial derivatives. Dirac processes add spikes to the existing building blocks of diffusions and jumps. Dirac processes are Generalized Processes, which have not been used directly before because the dollar value of non-Real numbers is meaningless. However, short-rate pricing is based on integrals so Dirac processes are natural. This integration directly implies that jumps are redundant whilst Dirac processes expand expressivity of short-rate approaches. Practically, we demonstrate that Dirac processes enable high implied volatility for CDS swaptions that has been otherwise problematic in hazard rate setups.
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中文摘要：
我们引入狄拉克过程，使用狄拉克三角函数，为金融衍生品的短期利率类型定价。狄拉克过程为扩散和跳跃的现有构造块添加了尖峰。狄拉克过程是广义过程，以前没有直接使用过，因为非实数的美元价值没有意义。然而，短期利率定价是基于积分的，所以狄拉克过程是自然的。这种整合直接意味着跳跃是多余的，而Dirac过程扩展了短速率方法的表达能力。实际上，我们证明了Dirac过程为CDS互换期权带来了高隐含波动性，而CDS互换期权在风险率设置中一直存在问题。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Pricing of Securities 证券定价
分类描述：Valuation and hedging of financial securities, their derivatives, and structured products
金融证券及其衍生产品和结构化产品的估值和套期保值
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一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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一级分类：Quantitative Finance 数量金融学
二级分类：Mathematical Finance 数学金融学
分类描述：Mathematical and analytical methods of finance, including stochastic, probabilistic and functional analysis, algebraic, geometric and other methods
金融的数学和分析方法，包括随机、概率和泛函分析、代数、几何和其他方法
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