[论文解读] Funding, Collateral and Hedging: uncovering the mechanics and the subtleties of funding valuation adjustments

Andrea Pallavicini, Daniele Perini+1 more|arXiv (Cornell University)|Oct 14, 2012

Stochastic processes and financial applications被引用 6

一句话总结

本文提出了一种统一的、风险中性衍生品定价框架，一致地整合了融资成本、保证金、信用估值调整（CVA）和债务估值调整（DVA），并基于递归的、非加性的定价方程实现。核心贡献在于表明，融资估值调整（FVA）不能被视作简单的加法项，且融资成本与DVA存在内在关联，从而否定了文献中常见的简化处理方式。

ABSTRACT

The main result of this paper is a collateralized counterparty valuation adjusted pricing equation, which allows to price a deal while taking into account credit and debit valuation adjustments (CVA, DVA) along with margining and funding costs, all in a consistent way. Funding risk breaks the bilateral nature of the valuation formula. We find that the equation has a recursive form, making the introduction of a purely additive funding valuation adjustment (FVA) difficult. Yet, we can cast the pricing equation into a set of iterative relationships which can be solved by means of standard least-square Monte Carlo techniques. As a consequence, we find that identifying funding costs and debit valuation adjustments is not tenable in general, contrary to what has been suggested in the literature in simple cases. The assumptions under which funding costs vanish are a very special case of the more general theory. We define a comprehensive framework that allows us to derive earlier results on funding or counterparty risk as a special case, although our framework is more than the sum of such special cases. We derive the general pricing equation by resorting to a risk-neutral approach where the new types of risks are included by modifying the payout cash flows. We consider realistic settings and include in our models the common market practices suggested by ISDA documentation, without assuming restrictive constraints on margining procedures and close-out netting rules. In particular, we allow for asymmetric collateral and funding rates, and exogenous liquidity policies and hedging strategies. Re-hypothecation liquidity risk and close-out amount evaluation issues are also covered. Finally, relevant examples of non-trivial settings illustrate how to derive known facts about discounting curves from a robust general framework and without resorting to ad hoc hypotheses.

研究动机与目标

• 开发一种一致的、风险中性的定价框架，无需人为假设即可整合融资成本、保证金、CVA与DVA。
• 解决现有文献中将FVA视为对无风险价格的简单加法调整所导致的不一致性问题。
• 阐明融资成本与DVA之间的相互依赖关系，挑战二者可分离的普遍假设。
• 形式化在现实市场实践（包括非对称融资与保证金利率）下定价方程的递归性质。
• 构建一个通用模型，涵盖并扩展先前关于折现、保证金与对手方风险的研究成果。

提出的方法

• 推导出一种嵌入融资、保证金与对手方风险的抵押双边估值调整定价（CBVA）方程，通过修改现金流实现，而非改变测度或折现方法。
• 采用风险中性方法，将融资与保证金成本作为显式现金流建模，以保持经典无套利定价理论的完整性。
• 引入一个无法以闭式解法求解的递归定价方程，需借助最小二乘蒙特卡洛等迭代数值方法求解。
• 通过两种不同渠道建模融资：银行内部资金池（内部融资）与外部市场融资，二者具有不同的利率与流动性政策。
• 整合ISDA文件中规定的现实市场实践，包括非对称保证金与融资利率、再抵押（rehypothecation）及终止净额结算规则。
• 证明融资利率并非无风险利率，且OIS利率并非融资利率的有效代理，除非在高度限制性假设下。

实验结果

研究问题

• RQ1 能否在衍生品定价中将融资估值调整（FVA）有意义地作为独立项加总到无风险价格之上？
• RQ2 非对称的融资与保证金利率在一致且无套利的框架下如何影响衍生品合约的定价？
• RQ3 在何种条件下融资成本可被视为与债务估值调整（DVA）独立，而在何种情况下二者存在内在关联？
• RQ4 为何标准的加法分解公式（价格 = 无风险价格 + CVA - CVA + FVA）在存在融资风险时会失效？
• RQ5 如何构建一个通用的定价框架，统一处理融资、保证金与对手方风险，而无需依赖限制性假设？

主要发现

• 包含融资、保证金与对手方风险的衍生品合约定价方程本质上是递归的，无法通过简单加法调整求解，从而否定了常见的FVA加法处理方式。
• 一般情况下，融资成本与DVA不可分离；将二者视为独立项会导致错误定价，尤其在融资风险与违约风险相关时更为显著。
• 文献中常采用的‘融资成本可忽略’假设仅在极不现实的条件下成立，如融资利差为零且内部资金池完全整合。
• 无风险利率并不等同于隔夜拆款利率（如OIS），将OIS视为融资利率会导致对FVA不存在性的错误结论。
• 该框架表明，由于不同机构的融资与保证金政策不同，同一笔交易可能对不同机构产生不同价格，从而破坏价格唯一性。
• 该模型从第一性原理出发，稳健地推导出折现曲线，无需人为假设，并将早期成果作为特例涵盖其中。