信贷、融资和错误路径风险下双边现金流的脆弱衍生品合约分析估值

Juan Jose Francisco Miguelez, Cristin Buescu
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引用次数: 0

摘要

我们研究了在存在资金、信用和错误风险的情况下,交易双方之间存在双边现金流的脆弱衍生品的估值问题,并推导了现价(ATM)远期合约的封闭形式估值公式以及一般情况下的二阶近似。我们假设了一个具有异质利率和违约发生的模型,并推断了合约违约前估值函数的柯西问题,其中包括从头开始计算任何交易对手风险-而不是计算估值调整统称为XVA。在将柯西问题线性化的特定资助政策下,我们获得了违约前估值的一般概率表示(定理1)。我们将这个一般框架应用于股权远期的估值,并建立了合约可以表示为在特定概率度量下适当选择罢工和到期日的欧式期权的连续投资组合(定理2)。当远期合约为ATM时,我们的估值公式允许一个封闭的形式表达式(推论2),并且我们推导了二阶近似模型的数值结果表明,远期合约对融资因素比信用因素更敏感,而较高的股票融资成本增加了对信用利差和错误风险的敏感性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Analytical valuation of vulnerable derivative contracts with bilateral cash flows under credit, funding and wrong-way risks
We study the problem of valuing a vulnerable derivative with bilateral cash flows between two counterparties in the presence of funding, credit and wrong-way risks, and derive a closed-form valuation formula for an at-the-money (ATM) forward contract as well as a second order approximation for the general case. We posit a model with heterogeneous interest rates and default occurrence and infer a Cauchy problem for the pre-default valuation function of the contract, which includes ab initio any counterparty risk - as opposed to calculating valuation adjustments collectively known as XVA. Under a specific funding policy which linearises the Cauchy problem, we obtain a generic probabilistic representation for the pre-default valuation (Theorem 1). We apply this general framework to the valuation of an equity forward and establish the contract can be expressed as a continuous portfolio of European options with suitably chosen strikes and expiries under a particular probability measure (Theorem 2). Our valuation formula admits a closed-form expression when the forward contract is ATM (Corollary 2) and we derive a second order approximation in moneyness when the contract is close to ATM (Theorem 3). Numerical results of our model show that the forward is more sensitive to funding factors than credit ones, while higher stock funding costs increase sensitivity to credit spreads and wrong-way risk.
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