英文标题：
《Optimal valuation of American callable credit default swaps under
drawdown of L\\\'evy insurance risk process》
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作者：
Zbigniew Palmowski and Budhi Surya
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最新提交年份：
2020
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英文摘要：
This paper discusses the valuation of credit default swaps, where default is announced when the reference asset price has gone below certain level from the last record maximum, also known as the high-water mark or drawdown. We assume that the protection buyer pays premium at fixed rate when the asset price is above a pre-specified level and continuously pays whenever the price increases. This payment scheme is in favour of the buyer as she only pays the premium when the market is in good condition for the protection against financial downturn. Under this framework, we look at an embedded option which gives the issuer an opportunity to call back the contract to a new one with reduced premium payment rate and slightly lower default coverage subject to paying a certain cost. We assume that the buyer is risk neutral investor trying to maximize the expected monetary value of the option over a class of stopping time. We discuss optimal solution to the stopping problem when the source of uncertainty of the asset price is modelled by L\\\'evy process with only downward jumps. Using recent development in excursion theory of L\\\'evy process, the results are given explicitly in terms of scale function of the L\\\'evy process. Furthermore, the value function of the stopping problem is shown to satisfy continuous and smooth pasting conditions regardless of regularity of the sample paths of the L\\\'evy process. Optimality and uniqueness of the solution are established using martingale approach for drawdown process and convexity of the scale function under Esscher transform of measure. Some numerical examples are discussed to illustrate the main results.
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中文摘要：
本文讨论了信用违约掉期的估值问题，即当参考资产价格低于上一次最高记录的某个水平时，即高水位或支取时，宣布违约。我们假设，当资产价格高于预先规定的水平时，保护买方以固定利率支付溢价，并在价格上涨时持续支付。这种支付方案有利于买方，因为买方只在市场状况良好时支付保险费，以抵御金融危机。在此框架下，我们研究了一种嵌入期权，该期权使发行人有机会在支付一定成本的前提下，以较低的保费支付率和略低的违约覆盖率收回新合同。我们假设买方是风险中性投资者，试图在一类停止时间内最大化期权的预期货币价值。我们讨论了当资产价格的不确定性来源由仅具有向下跳跃的L拞vy过程建模时，停止问题的最优解。利用列维过程漂移理论的最新发展，根据列维过程的标度函数明确给出了结果。此外，停止问题的值函数被证明满足连续和平滑的粘贴条件，而不管L拞vy过程的样本路径是否规则。在Esscher测度变换下，利用鞅方法对水位下降过程和尺度函数的凸性建立了解的最优性和唯一性。通过数值算例说明了主要结果。
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分类信息：

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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