Derivatives Discounting Explained

Repo convexity

There is an observed basis between repo discounting, implied from market repo rates, and bond discounting, stripped from the market prices of the underlying bonds. Here, this basis is explained as a convexity effect arising from the decorrelation between the discount rates for derivatives and bonds. Using a Hull-White model for the discount basis, expressions are derived that can be used to interpolate the repo rates of bonds with different maturities and to extrapolate the repo curve for discounting bond-collateralised derivatives.

Discounting with Imperfect Collateral

Cash collateral is perfect in that it provides simultaneous counterparty credit risk protection and derivatives funding. Securities are imperfect collateral, because of collateral segregation or differences in CSA haircuts and repo haircuts. Moreover, the collateral rate term structure is not observable in the repo market, for derivatives netting sets are perpetual while repo tenors are typically in months. This article synthesizes these effects into a derivative financing rate that replaces the risk-free discount rate. A break-even repo formulae is employed to supply non-observable collateral…

两条曲线，一个价格：定价和对冲利率衍生品解耦的远期和贴现收益率曲线

Two Curves, One Price: Pricing & Hedging Interest Rate Derivatives Decoupling Forwarding and Discounting Yield Curves

我们重新审视了单一货币利率衍生品的定价和对冲问题，使用多个不同的收益率曲线的贴现因子和远期利率与不同的基础利率期限的市场一致性估计。在2007年夏季信贷危机爆发后市场采用的这种双曲线-单一货币框架内，标准的单曲线无套利关系不再有效，可以通过适当考虑从市场基差掉期中提取的远期基差来恢复。数值结果表明，由此产生的远期基差曲线可能会显示出更丰富的微观期限结构，这可能会对利率工具的价格产生明显的影响。通过外汇类比，我们还得到了一般的无套利双曲线市场的公式，特别是基本的普通利率衍生品，FRA，掉期，上限/下限和掉期。这些表达式包括交叉货币衍生品的典型量子调整，自然源于与两条收益率曲线相关的数值之间的变化，这带来了波动性和相关性。数值情景证实了这种修正是不可忽略的，因此原则上，未经调整的双曲线价格并非没有套利。远期基础和定量调整都可以从交易对手风险的角度找到一个自然的财务解释。

无惧贴现——如何管理从EONIA到ESTR的过渡

No Fear of Discounting - How to Manage the Transition from EONIA to ESTR

研究金融基准改革中从EONIA到ESTR的过渡，详细展示其对多种金融产品定价的影响，采用基于ESTR的“净贴现”方法，确保金融行业能安全一致地转换欧元场外衍生品，对消除EONIA至关重要。

Coherent CVA and FVA with Liability Side Pricing of Derivatives

This article presents FVA and CVA of a bilateral derivative in a coherent manner, based on recent developments in fair value accounting and ISDA standards. We argue that a derivative liability, after primary risk factors being hedged, resembles in economics an issued variable funding note, and should be priced at the market rate of the issuer's debt. For the purpose of determining the fair value, the party on the liability side is economically neutral to make a deposit to the other party, which earns his current debt rate and effectively provides funding and hedging for the party holding the d…

信贷紧缩后的利率：多重曲线香草衍生品和SABR

Interest Rates After The Credit Crunch: Multiple-Curve Vanilla Derivatives and SABR

我们提出了一个定量研究的市场和模型的演变在信贷危机。特别是，我们专注于固定收益市场，我们分析了最相关的实证证据，关于Libor和OIS利率之间的分歧，基差互换利差的爆炸，以及抵押品协议和CSA贴现的扩散，在信贷和流动性影响方面。我们还回顾了从业者中流行的新的现代定价方法，该方法基于反映不同期限的Libor利率的不同信用和流动性风险的多个收益率曲线，以及每日保证金抵押品下衍生品交易产生的现金流的隔夜贴现。本文给出了经典和现代的无套利利率衍生品定价公式，并对具有随机波动率的市场标准SABR模型进行了多曲线推广。然后，我们报告的实证分析结果最近的市场数据比较前和后信贷紧缩的定价方法，并显示从古典到现代框架的市场实践的过渡。特别是，我们证明了利率互换市场已经放弃了自2010年3月以来的经典单曲线定价方法，典型的信贷紧缩前的利率世界，并采用了现代的多曲线CSA方法，从而将信用和流动性的影响到市场价格。同样的分析适用于欧洲上限/下限，发现全面过渡到现代多曲线CSA方法已推迟到2010年8月。最后，我们展示了稳健的SABR模型校准市场波动率微笑一致的新的市场证据。