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考虑信用、抵押品与资金成本的非线性衍生品估值

文章 arXiv papers · 作者: Damiano Brigo et al.
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总结

本文提出一个风险中性框架，用于在抵押品条款、交易对手信用敞口和资金成本影响现金流时对衍生品定价。该框架纳入信用估值、借方估值、流动性及资金估值调整，并说明不对称资金条款和违约平仓规则可能使价格呈递归且非线性。由于 CVA 和 FVA 等常见调整可能相互重叠，简单相加会导致风险重复计算；作者提出非线性调整来处理这一问题。

估值可表示为后向随机微分方程或半线性偏微分方程，随后改写为适用于最小二乘蒙特卡洛的迭代方程。一个广义 Black–Scholes 期权案例研究发现，资金风险会显著影响价格，重复计算也不可忽视。文章还讨论了中央清算、保证金安排以及非线性定价的更广泛影响。数值证据来自案例研究，因此本文未证明所有产品或市场惯例都会受到普遍性的价格影响。

核心观点

  • 抵押品、交易对手信用风险和资金成本会改变衍生品现金流与估值。
  • 不对称资金条款和违约平仓条款可能使双边定价呈非线性且具有递归性。
  • CVA 和 FVA 通常并非相互独立、可直接相加的调整，因此存在重复计算风险。
  • 定价方程可用最小二乘蒙特卡洛迭代求解。
  • 广义 Black–Scholes 案例研究发现资金影响不可忽视，并指出重复计算问题。

标签

衍生品定价期权风险管理回测统计学
全文
# Nonlinear Valuation under Collateral, Credit Risk and Funding Costs: A Numerical Case Study Extending Black-Scholes


# Nonlinear Valuation under Collateral, Credit Risk and Funding Costs: A Numerical Case Study Extending Black-Scholes









We develop an arbitrage-free framework for consistent valuation of derivative trades with collateralization, counterparty credit gap risk, and funding costs, following the approach first proposed by Pallavicini and co-authors in 2011. Based on the risk-neutral pricing principle, we derive a general pricing equation where Credit, Debit, Liquidity and Funding Valuation Adjustments (CVA, DVA, LVA and FVA) are introduced by simply modifying the payout cash-flows of the deal. Funding costs and specific close-out procedures at default break the bilateral nature of the deal price and render the valuation problem a non-linear and recursive one. CVA and FVA are in general not really additive adjustments, and the risk for double counting is concrete. We introduce a new adjustment, called a Non-linearity Valuation Adjustment (NVA), to address double-counting. The theoretical risk free rate disappears from our final equations. The framework can be tailored also to CCP trading under initial and variation margins, as explained in detail in Brigo and Pallavicini (2014). In particular, we allow for asymmetric collateral and funding rates, replacement close-out and re-hypothecation. The valuation equation takes the form of a backward stochastic differential equation or semi-linear partial differential equation, and can be cast as a set of iterative equations that can be solved by least-squares Monte Carlo. We propose such a simulation algorithm in a case study involving a generalization of the benchmark model of Black and Scholes for option pricing. Our numerical results confirm that funding risk has a non-trivial impact on the deal price, and that double counting matters too. We conclude the article with an analysis of large scale implications of non-linearity of the pricing equations.

在遵守原作品许可的前提下，附作者信息全文展示。 许可协议: abstract CC0

此摘要由 Stratmill 研究智能体根据原文撰写，并非原文副本。