SSRN Author: Damiano BrigoDamiano Brigo SSRN Content
http://www.ssrn.com/author=268434
http://www.ssrn.com/rss/en-usSun, 21 Feb 2016 01:37:06 GMTeditor@ssrn.com (Editor)Sun, 21 Feb 2016 01:37:06 GMTwebmaster@ssrn.com (WebMaster)SSRN RSS Generator 1.0New: Funding, Repo and Credit Inclusion in Option Pricing via DividendsThis paper specializes a number of earlier contributions to the theory of valuation of financial products in presence of credit risk, repurchase agreements and funding costs. Earlier works, including our own, pointed to the need of tools such as Backward Stochastic Differential Equations (BSDEs) or semi-linear Partial Differential Equations (PDEs), which in practice translate to ad-hoc numerical methods that are time-consuming and which render the full valuation and risk analysis difficult. We specialize here the valuation framework to benchmark derivatives and we show that, under a number of simplifying assumptions, the valuation paradigm can be recast as a Black-Scholes model with dividends. In turn, this allows for a detailed valuation analysis, stress testing and risk analysis via sensitivities. We refer to the full paper for a more complete mathematical treatment.
http://www.ssrn.com/abstract=2734459
http://www.ssrn.com/1471962.htmlSat, 20 Feb 2016 16:20:51 GMTREVISION: Multi Currency Credit Default Swaps: Quanto Effects and FX Devaluation JumpsCredit Default Swaps (CDS) on a reference entity may be traded in multiple currencies, in that protection upon default may be offered either in the domestic currency where the entity resides, or in a more liquid and global foreign currency. In this situation currency fluctuations clearly introduce a source of risk on CDS spreads. For emerging markets, but in some cases even in well developed markets, the risk of dramatic Foreign Exchange (FX) rate devaluation in conjunction with default events is relevant. We address this issue by proposing and implementing a model that considers the risk of foreign currency devaluation that is synchronous with default of the reference entity. As a fundamental example we consider the sovereign CDSs on Italy, quoted both in EUR and USD.
Preliminary results indicate that perceived risks of devaluation can induce a significant basis across domestic and foreign CDS quotes. For the Republic of Italy, a USD CDS spread quote of 440 bps can translate into ...
http://www.ssrn.com/abstract=2703605
http://www.ssrn.com/1455020.htmlTue, 22 Dec 2015 12:13:16 GMTREVISION: Multi Currency Credit Default Swaps: Quanto Effects and FX Devaluation JumpsCredit Default Swaps (CDS) on a reference entity may be traded in multiple currencies, in that protection upon default may be offered either in the domestic currency where the entity resides, or in a more liquid and global foreign currency. In this situation currency fluctuations clearly introduce a source of risk on CDS spreads. For emerging markets, but in some cases even in well developed markets, the risk of dramatic Foreign Exchange (FX) rate devaluation in conjunction with default events is relevant. We address this issue by proposing and implementing a model that considers the risk of foreign currency devaluation that is synchronous with default of the reference entity. As a fundamental example we consider the sovereign CDSs on Italy, quoted both in EUR and USD.
Preliminary results indicate that perceived risks of devaluation can induce a significant basis across domestic and foreign CDS quotes. For the Republic of Italy, a USD CDS spread quote of 440 bps can translate into ...
http://www.ssrn.com/abstract=2703605
http://www.ssrn.com/1453409.htmlWed, 16 Dec 2015 12:24:05 GMTNew: The Multivariate Mixture Dynamics Model: Shifted Dynamics and Correlation SkewThe Multi Variate Mixture Dynamics model is a tractable, dynamical, arbitrage-free multivariate model characterized by transparency on the dependence structure, since closed form formulae for terminal correlations, average correlations and copula function are available. It also allows for complete decorrelation between assets and instantaneous variances. Each single asset is modelled according to a lognormal mixture dynamics model, and this univariate version is widely used in the industry due to its flexibility and accuracy. The same property holds for the multivariate process of all assets, whose density is a mixture of multivariate basic densities. This allows for consistency of single asset and index/portfolio smile.
In this paper, we generalize the MVMD model by introducing shifted dynamics and we propose a definition of implied correlation under this model. We investigate whether the model is able to consistently reproduce the implied volatility of FX cross rates, once the ...
http://www.ssrn.com/abstract=2703722
http://www.ssrn.com/1453178.htmlWed, 16 Dec 2015 02:38:08 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/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 GMT