Collateral Agreements Research Articles

A Consistent Pricing Framework with Counterparty Risk and Collateral Agreements

We study in this article the pricing of a derivate contract in presence of both counterparty risk and collateral posting rules. We come up with a new pricing framework that generalizes the works of Piterbarg and Kjaer-Burgard. An application to a Total Return Swap will show that hard numerical complications could arise in the presence collateral when pricing the counter-party risk. A hybrid numerical method based on finite differences and Monte Carlo is used to cope with the problem.

Self-Funding Portfolios and Collateralised Derivative Pricing

A general framework is proposed for including the effects of collateral management in derivative pricing. Comprehensive yet simple formulas are obtained allowing the impact of different types of collateral agreements to be incorporated in valuations. The approach centers on analysing the self-financing condition on portfolios which explicitly include the market funding of derivative, collateral and hedging positions. Major simplifications, including a martingale pricing formula, are obtained when funding and collateral are in the form of cash, but the general framework aims at greater generality. The functional dependence of the collateral balance on the value of the derivative also plays a central role in the analysis. The “institutional” implications for liquidity management (pertaining to derivative desk funding, bank treasury “transfer pricing,” and the interplay with the repo market) are briefly considered.

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 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 subportfolio is self-financing on its own, rather than the whole portfolio. The error in the first paper is avoided when clearly distinguishing between price processes, dividend processes and gain processes. We present an outline of the derivation that yields the correct statement of the self-financing condition, clarifying the structure of the relevant funding accounts, and show that the final result in beyond discounting is correct, even if the self-financing condition stated is not.

Wrong Way Risk and Jump to Default

After Lehman collapse, the market began to consider the potential default of big instituions classified too big to default. The CVA and collateral agreement became a market standard. One major risk of the Credit Risk Measure is the Wrong Way Risk. We will try to define the phenomena trough concret examples. Indeed it could afect the portfolio value but also the collateral value.The main task of this paper is to introduce an efficient model of default able to give realistic path and low variance estimator.

Pricing of Derivatives Contracts Under Collateral Agreements: Liquidity and Funding Value Adjustments

We analyse the pricing of derivatives under a CSA agreement, without considering netting, minimum transfer amounts and thresholds. We come up with a decomposition of the total contract's value in a risk-free component, a liquidity value adjustment and a funding value adjustment. Implications for the organization of a dealing room are also investigated.

Pricing Swaps Including Funding Costs

In this paper we study how to include funding costs into the pricing of interest rate swaps and we show how they affect the value of the swap via a Funding Value Adjustment (FVA), in analogy with the Credit Value Adjustment (CVA) and the DVA. We consider the pricing of swap contracts with no collateral agreement or any other form of credit risk mitigations.

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

We present a quantitative study of the markets and models evolution across the credit crunch crisis. In particular, we focus on the fixed income market and we analyze the most relevant empirical evidences regarding the divergences between Libor and OIS rates, the explosion of Basis Swaps spreads, and the diffusion of collateral agreements and CSA-discounting, in terms of credit and liquidity effects. We also review the new modern pricing approach prevailing among practitioners, based on multiple yield curves reflecting the different credit and liquidity risk of Libor rates with different tenors and the overnight discounting of cash flows originated by derivative transactions under collateral with daily margination. We report the classical and modern no-arbitrage pricing formulas for plain vanilla interest rate derivatives, and the multiple-curve generalization of the market standard SABR model with stochastic volatility. We then report the results of an empirical analysis on recent market data comparing pre- and post-credit crunch pricing methodologies and showing the transition of the market practice from the classical to the modern framework. In particular, we prove that the market of Interest Rate Swaps has abandoned since March 2010 the classical Single-Curve pricing approach, typical of the pre-credit crunch interest rate world, and has adopted the modern Multiple-Curve CSA approach, thus incorporating credit and liquidity effects into market prices. The same analysis is applied to European Caps/Floors, finding that the full transition to the modern Multiple-Curve CSA approach has retarded up to August 2010. Finally, we show the robustness of the SABR model to calibrate the market volatility smile coherently with the new market evidences.

Modeling of Interest Rate Term Structures Under Collateralization and its Implications

In recent years, we have observed dramatic increase of collateralization as an important credit risk mitigation tool in over the counter (OTC) market [6]. Combined with the significant and persistent widening of various basis spreads, such as Libor-OIS and cross currency basis, the practitioners have started to notice the importance of difference between the funding cost of contracts and Libors of the relevant currencies. In this article, we integrate the series of our recent works [1, 2, 4] and explain the consistent construction of term structures of interest rates in the presence of collateralization and all the relevant basis spreads, their no-arbitrage dynamics as well as their implications for derivative pricing and risk management. Particularly, we have shown the importance of the choice of collateral currency and embedded cheapest-to-deliver (CTD) option in a collateral agreement.

Collateral Informant Assessment in Alcohol Use Research Involving College Students

Objective: This study examined the associations between college students’ self-reported alcohol use and corresponding collateral reports and identified factors that influence agreement between both sets of reports. Participants/Methods: Subject–collateral pairs (N = 300) were recruited from undergraduate psychology courses. Results: Data yielded moderate correlations between subject-collateral pairs for all alcohol use measures, whereas discrepancy analyses revealed a tendency for subjects to report greater alcohol use relative to collateral reports. Greater subject–collateral agreement regarding frequency of subject alcohol use was predicted by a greater frequency of shared drinking occasions between the dyads, lower subject self-reported drug use, and lower levels of collateral guessing, whereas greater correspondence for quantity of alcohol consumed was predicted by fewer subject self-reported alcohol-related negative consequences, lower levels of subject self-reported drug use, and lower levels of alcohol ingestion among collaterals. Conclusions: College students appear to provide reasonably accurate self-reports of their alcohol use.

Collateral Posting and Choice of Collateral Currency - Implications for Derivative Pricing and Risk Management

In recent years, we have observed the dramatic increase of the use of collateral as an important credit risk mitigation tool. It has become even rare to make a contract without collateral agreement among the major financial institutions. In addition to the significant reduction of the counterparty exposure, collateralization has important implications for the pricing of derivatives through the change of effective funding cost. This paper has demonstrated the impact of collateralization on the derivative pricing by constructing the term structure of swap rates based on the actual market data. It has also shown the importance of the ”choice” of collateral currency. Especially, when the contract allows multiple currencies as eligible collateral and free replacement among them, the paper has found that the embedded ”cheapest-to-deliver” option can be quite valuable and significantly change the fair value of a trade. The implications of these findings for market risk management have been also discussed.

A Note on Construction of Multiple Swap Curves with and without Collateral

There are now available wide variety of swap products which exchange Libors with different currencies and tenors. Furthermore, the collateralization is becoming more and more popular due to the increased attention to the counter party credit risk. These developments require clear distinction among different type of Libors and the discounting rates. In this brief note, we will explain the method to construct the multiple swap curves consistently with all the relevant swaps with and without a collateral agreement.

Gender effects on client–spousal collateral agreement levels in substance abuse posttreatment reports

This study examines gender effects on client–spousal collateral agreement in substance abuse posttreatment reports and assesses the dependability of spousal collaterals in corroborating these reports. Study participants included 178 male clients with female spousal collaterals (male client dyads) and 58 female clients with male spousal collaterals (female client dyads) who completed follow-up interviews 6 months post admission. Interviews were conducted from July 2002 to June 2004. Levels of agreement were examined by dyad type for responses to 13 questions regarding clients’ treatment experiences and treatment effectiveness. A simple kappa coefficient was calculated to measure the degree of nonchance agreement between clients and their spouses using SAS/Base, SAS/Stat, and SAS/IML. Agreement levels between the two dyads were compared and examined whether gender differences in agreement levels were significant. Agreement levels were found to be high, ranging from 80.4 to 97.1% for male client dyads and from 76.5 to 100% for female client dyads. Six of the 13 questions for male client dyads and 8 of the 13 questions for female client dyads revealed excellent or substantial nonchance agreement. Questions related to domestic violence had poor nonchance agreement, with “Victim of domestic violence since treatment” having the lowest score for the male client dyad. Only one question, “Currently on probation or parole,” showed a significant difference across genders, as males revealed a significantly higher level of agreement. Moderate to substantial agreement was determined for 11 out of the 13 questions regardless of gender effects. This study provides empirical data affirming the high dependability of spousal collaterals to validate responses about clients’ substance abuse following treatment. However, the study revealed a high degree of disagreement among both male client dyads and female client dyads regarding questions related to domestic violence (including whether the client had committed or been a victim of domestic violence). Following rigorous gender analyses, this study reveals little difference overall in agreement levels between gender dyads.

Factors associated with client–collateral agreement in substance abuse post-treatment self-reports

This study examined levels of agreement and directionality of disagreement between the post-treatment self-reports of substance abuse clients and their collaterals. The study population comprised 1252 clients with a primary or secondary diagnosis of substance abuse or dependence whose treatment was publicly funded in Tennessee. Client and collateral responses to 13 questions were analyzed for levels of agreement, revealing the following: (a) levels of client–collateral agreement were high, at least 75% agreement on all 13 questions and at least 88% agreement on 10 variables; (b) a Simple Kappa Test confirmed that 11 out of 13 items had moderate to excellent nonchance agreement; (c) there was no consistent trend in directionality, that is, clients neither reported information more positively nor more negatively than their collaterals did; (d) on average, those collaterals who were spouses, parents, and children agreed more with clients compared to other types of collaterals; and (e) those collaterals who saw the clients more frequently and more recently had higher agreement than those who saw the clients less frequently. This research reaffirms that collaterals are a valuable source for verifying the accuracy of clients' self-reports and that this approach continues to hold considerable promise for substance abuse post-treatment assessment.

Underleases and collateral agreements

Underleases and collateral agreements

The Gold Collateral Agreement and its Aftermath ‐ Implications for South Africa

The Gold Collateral Agreement and its Aftermath ‐ Implications for South Africa

Domestic Relations. Separation Agreement Invalidated by Collateral Oral Agreement to Obtain a Divorce

Domestic Relations. Separation Agreement Invalidated by Collateral Oral Agreement to Obtain a Divorce

The Enforcement of Collateral Agreements between the Secured Creditor and the Bankrupt

The Enforcement of Collateral Agreements between the Secured Creditor and the Bankrupt

Specific Performance: Effect of a Vendor's Breach of a Collateral Agreement

Specific Performance: Effect of a Vendor's Breach of a Collateral Agreement

Contracts: Illegality: Collateral Agreements under Home Owners' Loan Act

Contracts: Illegality: Collateral Agreements under Home Owners' Loan Act

Bills and Notes: Alteration by Collateral Written Agreement

Bills and Notes: Alteration by Collateral Written Agreement