随机波动率模型中的CVA和脆弱期权
CVA and vulnerable options in stochastic volatility models
摘要：
在这项工作中，我们希望提供一个一般原则，以评估CVA（信用价值调整）的脆弱的选项，这是一个选项受到一些违约事件，有关的解决方案的发行人。CVA是正确评估合同所必需的，尤其是在存在错误风险（WWR）的情况下，当信用恶化决定索赔价格的增加时，CVA就显得尤为重要。特别是，我们感兴趣的是评估CVA的随机波动率模型的基础价格（这往往适合相当好的市场价格）时，承认与违约事件的相关性。巧妙地利用Ito的演算，我们给出了一个适用于SABR、Hull & White和Heston等流行模型的一般表示公式，该公式明确地表明了CVA中由于过程相关而引起的修正.之后，我们专门化这个公式，并构造它的近似为三个选定的模型。最后，我们进行了数值研究，以测试公式的准确性，比较我们的结果与蒙特卡罗模拟。
英文摘要：
In this work we want to provide a general principle to evaluate the CVA (Credit Value Adjustment) for a vulnerable option, that is an option subject to some default event, concerning the solvability of the issuer. CVA is needed to evaluate correctly the contract and it is particularly important in presence of WWR (Wrong Way Risk), when a credit deterioration determines an increase of the claim's price. In particular, we are interested in evaluating the CVA in stochastic volatility models for the underlying's price (which often fit quite well the market's prices) when admitting correlation with the default event. By cunningly using Ito's calculus, we provide a general representation formula applicable to some popular models such as SABR, Hull \& White and Heston, which explicitly shows the correction in CVA due to the processes correlation. Later, we specialize this formula and construct its approximation for the three selected models. Lastly, we run a numerical study to test the formula's accuracy, comparing our results with Monte Carlo simulations.
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