考虑交易对手违约的单名LCDS定价及其CVA计算.doc

考虑交易对手违约的单名LCDS定价及其CVA计算 梁进，王涛，杨晓丽同济大学数学系，上海 摘要：分析了贷款信用违约互换的主要风险并建立了其定价模型。 在约化框架下，利用单因子反CIR模型来刻画早偿和违约的负相关性和非负性，并在此假定下得到定价公式的封闭解。 在此基础上考虑了交易对手可违约的单名贷款信用违约互换（LCDS）的信用价值调整（CVA）的计算模型，即在模型中加入LCDS卖方即交易对手的违约强度，并通过一个非线性偏微分方程对模型进行求解。最后，基于CVA计算模型和数值结果，还对错位风险作了讨论。 关键词：贷款信用违约互换约化模型单因子反CIR模型计算错位风险 Single name LCDS Pricing and Related CVA Calculation regarding Counterparty Default Institutional Client Group, Industrial Securities Co. Ltd., Shanghai 200135） Abstract: In this paper, under the reduced form framework, a pricing model for loan-only credit default swap (LCDS) with negative correlation between prepayment and default is established. Under reduced framework, by one factor inverse CIR model, we obtain a closed form pricing formula. Using this formula, a calculation scheme for credit value adjustment (CVA) for LCDS is given, where the counterparty risk of the LCDS is considered. Moreover, a wrong way risk related issue is discussed. The research conducted in this article indicates that the price of an LCDS contract with counterparty credit risk (CCR) is lower than one without CCR, and CVA increases with the termination of the LCDS, interest rate and the correlation between the reference loan and the counterparty. The spread for an LCDS with CCR is lower than that of a normal LCDS. If the reference loan is negatively correlated with the counterparty, CVA decreases with the absolute value of the correlation coefficient. Key Words: Loan-only Credit Default Swap, Reduced Form Framework, One Factor inverse CIR Model, CVA, Wrong Way Risk 贷款信用违约互换（LCDS）是在传统信用违约互换（CDS）基础上发展而来的一种金融衍生产品。一张LCDS合约涉及三方：合约的售出者A方，合约的购买者B方及贷款的发行者C方。借款人C 向银行B 申请抵押贷款，B 面临C 可能无法按时偿付本息的信用风险，于是B 与A 签订一张LCDS合约，参考债务为有抵押的贷款，A 为保护卖方，B 为保护买方。B 定期向A 支付保费，直至合约参考实体C 发生信用事件。在C 发生信用事件时，B 相应的损失由A 来承担。由于贷款是可提前偿付的，因此C亦可能提前偿还贷款而造成LCDS合约的提前终止，此时A方无须赔偿。LCDS担保的贷款不仅存在违约风险，同时存在早偿风险。这是LCDS和CDS最大的区别。 常用的LCDS定价框架一般有结构化方法和约化方法两种。吴森用结构化方法考虑公司资产与抵押品价值的变化LCDS进行定价。周宇晶使用约化方法Top down模型对一篮子LCDS产品进行定价。王涛。 大多数的场外衍生品交易都有交易对手的信用风险（ounterparty