Discounting with Imperfect Collateral

Illustrating a problem in the self-financing condition in two 2010-2011 papers on funding, collateral and discounting

We illustrate a problem in the self-financing condition used in the papers "Funding beyond discounting: collateral agreements and derivatives pricing" (Risk Magazine, February 2010) and "Partial Differential Equation Representations of Derivatives with Counterparty Risk and Funding Costs" (The Journal of Credit Risk, 2011). These papers state an erroneous self-financing condition. In the first paper, this is equivalent to assuming that the equity position is self-financing on its own and without including the cash position. In the second paper, this is equivalent to assuming that a subportfoli…

Pricing of Mexican Interest Rate Swaps in Presence of Multiple Collateral Currencies

The financial crisis of 2007/08 caused catastrophic consequences and brought a bunch of changes around the world. Interest rates that were known to follow or behave similarly of each other diverged. Furthermore, the regulation and in particular the counterparty credit risk began to to be considered and quantified. Consequently, pre-crisis models are no longer valid. Indeed, this work sets the basis to define a valid model that considers the post-crisis world assumptions for the Mexican swap market. The model used in this work was the proposed by Fujii, Shimada and Takahashi in [Fujii et. al., …

Derivative Pricing under Asymmetric and Imperfect Collateralization and CVA

The importance of collateralization through the change of funding cost is now well recognized among practitioners. In this article, we have extended the previous studies of collateralized derivative pricing to more generic situation, that is asymmetric and imperfect collateralization with the associated counter party credit risk. By introducing the collateral coverage ratio, our framework can handle these issues in an unified manner. Although the resultant pricing formula becomes non-linear FBSDE and cannot be solve exactly, the fist order approximation is provided using Gateaux derivative. We…

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.

Derivatives Discounting Explained

Derivative pricing is about cash flow discounting at the riskfree rate. This teaching has lost its meaning post the financial crisis, due to the addition of extra value adjustments (XVA), which also made derivatives pricing and valuation a very difficult task for investors. This article recovers a properly defined discount rate that corresponds to different collateral and margin schemes. A binomial tree model is developed, enabling end-users to price in counterparty default and funding risk. Coherent XVAs, if needed, naturally result from decomposing the discount rate, and can be computed on t…

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。