SSRN Author: Damiano BrigoDamiano Brigo SSRN Content
http://www.ssrn.com/author=268434
http://www.ssrn.com/rss/en-usSun, 29 Nov 2015 01:42:54 GMTeditor@ssrn.com (Editor)Sun, 29 Nov 2015 01:42:54 GMTwebmaster@ssrn.com (WebMaster)SSRN RSS Generator 1.0REVISION: Invariance, Existence and Uniqueness of Solutions of Nonlinear Valuation PDEs and FBSDEs Inclusive of Credit Risk, Collateral and Funding CostsWe study conditions for existence, uniqueness and invariance of the comprehensive nonlinear valuation equations first introduced in Pallavicini et al (2011). These equations take the form of semi-linear PDEs and Forward-Backward Stochastic Differential Equations (FBSDEs). After summarizing the cash flows definitions allowing us to extend valuation to credit risk and default closeout, including collateral margining with possible re-hypothecation, and treasury funding costs, we show how such cash flows, when present-valued in an arbitrage free setting, lead to semi-linear PDEs or more generally to FBSDEs. We provide conditions for existence and uniqueness of such solutions in a viscosity and classical sense, discussing the role of the hedging strategy. We show an invariance theorem stating that even though we start from a risk-neutral valuation approach based on a locally risk-free bank account growing at a risk-free rate, our final valuation equations do not depend on the risk free ...
http://www.ssrn.com/abstract=2613010
http://www.ssrn.com/1448428.htmlSat, 28 Nov 2015 15:02:32 GMTNew: Efficient Pricing of Default Risk: Different Approaches for a Single GoalWith the rapid development of the credit derivatives market, efficient pricing of default has become an extremely important issue for the credit risk management of banks and other investors. We consider here some of the opportunities and problems that the development of this market poses to quantitative research in academia and industry. We describe different modeling choices pointing out the practical pros and cons of the different frameworks. For all different frameworks, we present innovative solutions allowing both computational efficiency and high consistency with the increasingly liquid credit reference market, the market of credit default swaps.
http://www.ssrn.com/abstract=2691157
http://www.ssrn.com/1445273.htmlTue, 17 Nov 2015 06:47:15 GMTREVISION: Impact of Multiple Curve Dynamics in Credit Valuation Adjustments under CollateralizationWe present a detailed analysis of interest rate derivatives valuation under credit risk and collateral modeling. We show how the credit and collateral extended valuation framework in Pallavicini et al (2011), and the related collateralized valuation measure, can be helpful in defining the key market rates underlying the multiple interest rate curves that characterize current interest rate markets. A key point is that spot Libor rates are to be treated as market primitives rather than being defined by no-arbitrage relationships. We formulate a consistent realistic dynamics for the different rates emerging from our analysis and compare the resulting model performances to simpler models used in the industry. We include the often neglected margin period of risk, showing how this feature may increase the impact of different rates dynamics on valuation. We point out limitations of multiple curve models with deterministic basis considering valuation of particularly sensitive products such ...
http://www.ssrn.com/abstract=2638229
http://www.ssrn.com/1428019.htmlMon, 14 Sep 2015 13:06:11 GMTREVISION: Interest-Rate Modeling in Collateralized Markets: Multiple Curves and Credit-Liquidity EffectsWe present a detailed analysis of interest rate derivatives valuation under credit risk and collateral modeling. We show how the credit and collateral extended valuation framework in Pallavicini et al (2011), and the related collateralized valuation measure, can be helpful in defining the key market rates underlying the multiple interest rate curves that characterize current interest rate markets. A key point is that spot Libor rates are to be treated as market primitives rather than being defined by no-arbitrage relationships. We formulate a consistent realistic dynamics for the different rates emerging from our analysis and compare the resulting model performances to simpler models used in the industry. We include the often neglected margin period of risk, showing how this feature may increase the impact of different rates dynamics on valuation. We point out limitations of multiple curve models with deterministic basis considering valuation of particularly sensitive products such ...
http://www.ssrn.com/abstract=2638229
http://www.ssrn.com/1416407.htmlFri, 31 Jul 2015 14:46:13 GMTNew: The Capco Exit Probability Index (CEPIX): Methodology and History of an Index Expressing Euro Exit LikelihoodsThe Cepix (Capco Exit Probabilty Index) project aimed at providing the market with a quick summary index expressing the likelihood that each country in the Eurozone could leave the Euro. It was offered online for free from the end of 2012 to the end of 2014, for two years, at Capco dot com. The index follows a simple formula that combines information from sovereign bond yields, GDP and debt, and credit ratings. The main idea is to combine responsive but often too volatile market implied default probability information from bond prices with more stable but less responsive traditional credit ratings information. The weights in the combination are decided based on macroeconomic data, namely GDP and Debt. The index history on some key moments and entities helps illustrating the interesting features of the index methodology.
http://www.ssrn.com/abstract=2622631
http://www.ssrn.com/1407383.htmlFri, 26 Jun 2015 08:15:57 GMTREVISION: Invariance, Existence and Uniqueness of Solutions of Nonlinear Valuation PDEs and FBSDEs Inclusive of Credit Risk, Collateral and Funding CostsWe study conditions for existence, uniqueness and invariance of the comprehensive nonlinear valuation equations first introduced in Pallavicini et al (2011). These equations take the form of semi-linear PDEs and Forward-Backward Stochastic Differential Equations (FBSDEs). After summarizing the cash flows definitions allowing us to extend valuation to credit risk and default closeout, including collateral margining with possible re-hypothecation, and treasury funding costs, we show how such cash flows, when present-valued in an arbitrage free setting, lead to semi-linear PDEs or more generally to FBSDEs. We provide conditions for existence and uniqueness of such solutions in a viscosity and classical sense, discussing the role of the hedging strategy. We show an invariance theorem stating that even though we start from a risk-neutral valuation approach based on a locally risk-free bank account growing at a risk-free rate, our final valuation equations do not depend on the risk free ...
http://www.ssrn.com/abstract=2613010
http://www.ssrn.com/1401241.htmlTue, 02 Jun 2015 12:36:34 GMTREVISION: Macroeconomic-Based No-Arbitrage Dynamics for Inflation Securities ValuationWe develop a model to price inflation and interest rates derivatives using continuous-time dynamics that have some links with macroeconomic monetary DSGE models equipped with a Taylor rule: in particular, the reaction function of the central bank, the bond market liquidity, inflation and growth expectations play an important role. The model can explain the effects of non-standard monetary policies (like quantitative easing or its tapering) and shed light on how central bank policy can affect the value of inflation and interest rates derivatives.
The model is built under standard no-arbitrage assumptions. Interestingly, the model yields short rate dynamics that are consistent with a time-varying Hull-White model, therefore making the calibration to the nominal interest curve and options straightforward. Further, we obtain closed forms for both zero-coupon and year-on-year inflation swap and options. The calibration strategy we propose is fully separable, which means that the ...
http://www.ssrn.com/abstract=2417983
http://www.ssrn.com/1374289.htmlTue, 17 Feb 2015 09:31:06 GMTREVISION: An Initial Approach to Risk Management of Funding CostsIn this note we sketch an initial tentative approach to funding costs analysis and management for contracts with bilateral counterparty risk in a simplified setting. We depart from the existing literature by analyzing the issue of funding costs and benets under the assumption that the associated risks cannot be hedged properly. We also model the treasury funding spread by means of a stochastic Weighted Cost of Funding Spread (WCFS) which helps describing more realistic financing policies of a financial institution. We elaborate on some limitations in replication-based Funding/Credit Valuation Adjustments we worked on ourselves in the past, namely CVA, DVA, FVA and related quantities as generally discussed in the industry. We advocate as a different possibility, when replication is not possible, the analysis of the funding profit and loss distribution and explain how long term funding spreads, wrong way risk and systemic risk are generally overlooked in most of the current literature ...
http://www.ssrn.com/abstract=2507447
http://www.ssrn.com/1355132.htmlMon, 01 Dec 2014 13:47:15 GMT