使CVA模型适应Leland的框架
Adapting the CVA model to Leland's framework
摘要：
我们考虑了Burgard和Kjaer（2011）提出的框架，该框架推导出了PDE，该PDE控制了包括双边交易对手风险和融资在内的期权价格。我们通过放宽套期保值投资组合中不存在交易成本的假设，提出了与交易资产和交易价格成比例的成本来扩展这项工作。在得到非线性偏微分方程后，我们证明了相应的初边值问题解的存在性。此外，我们开发了一个数值方案，允许通过为模型的每个参数设置不同的值来找到PDE的解决方案。为了了解模型中每个变量的影响，我们分析了希腊期权和价格对所有风险因素变化的敏感性。
英文摘要：
We consider the framework proposed by Burgard and Kjaer (2011) that derives the PDE which governs the price of an option including bilateral counterparty risk and funding. We extend this work by relaxing the assumption of absence of transaction costs in the hedging portfolio by proposing a cost proportional to the amount of assets traded and the traded price. After deriving the nonlinear PDE, we prove the existence of a solution for the corresponding initial-boundary value problem. Moreover, we develop a numerical scheme that allows to find the solution of the PDE by setting different values for each parameter of the model. To understand the impact of each variable within the model, we analyze the Greeks of the option and the sensitivity of the price to changes in all the risk factors.
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