Publications
170 results found
Crepey S, Bielecki TR, Brigo D, 2014, Rating Triggers and Credit Migrations, COUNTERPARTY RISK AND FUNDING: A TALE OF TWO PUZZLES, Publisher: CRC PRESS-TAYLOR & FRANCIS GROUP, Pages: 279-296, ISBN: 978-1-4665-1645-8
Crepey S, Bielecki TR, Brigo D, 2014, A Unified Perspective, COUNTERPARTY RISK AND FUNDING: A TALE OF TWO PUZZLES, Publisher: CRC PRESS-TAYLOR & FRANCIS GROUP, Pages: 297-308, ISBN: 978-1-4665-1645-8
Crepey S, Bielecki TR, Brigo D, 2014, CVA Computations for One CDS in the Common-Shock Model, COUNTERPARTY RISK AND FUNDING: A TALE OF TWO PUZZLES, Publisher: CRC PRESS-TAYLOR & FRANCIS GROUP, Pages: 239-266, ISBN: 978-1-4665-1645-8
Crepey S, Bielecki TR, Brigo D, 2014, A Galilean Dialogue on Counterparty Risk, CVA, DVA, Multiple Curves, Collateral and Funding, COUNTERPARTY RISK AND FUNDING: A TALE OF TWO PUZZLES, Publisher: CRC PRESS-TAYLOR & FRANCIS GROUP, Pages: 3-45, ISBN: 978-1-4665-1645-8
Crepey S, Bielecki TR, Brigo D, 2014, Dynamic Gaussian Copula Model, COUNTERPARTY RISK AND FUNDING: A TALE OF TWO PUZZLES, Publisher: CRC PRESS-TAYLOR & FRANCIS GROUP, Pages: 169-191, ISBN: 978-1-4665-1645-8
Brigo D, Capponi A, Pallavicini A, 2013, ARBITRAGE-FREE BILATERAL COUNTERPARTY RISK VALUATION UNDER COLLATERALIZATION AND APPLICATION TO CREDIT DEFAULT SWAPS, Mathematical Finance, Vol: 24, Pages: 1252146-1252146, ISSN: 0960-1627
We develop an arbitrage-free valuation framework for bilateral counterparty risk, where collateral is included with possible rehypothecation. We show that the adjustment is given by the sum of two option payoff terms, where each term depends on the netted exposure, i.e., the difference between the on-default exposure and the predefault collateral account. We then specialize our analysis to credit default swaps (CDS) as underlying portfolios, and construct a numerical scheme to evaluate the adjustment under a doubly stochastic default framework. In particular, we show that for CDS contracts a perfect collateralization cannot be achieved, even under continuous collateralization, if the reference entity’s and counterparty’s default times are dependent. The impact of rehypothecation, collateral margining frequency, and default correlation-induced contagion is illustrated with numerical examples.
Brigo D, Armstrong J, 2013, Stochastic filtering by projection: the example of the cubic sensor, Geometric Science of Information: First International Conference, Pages: 685-692
The “projection method” is an approach to finding numerical approximations to the optimal filter for non linear stochastic filtering problems. One uses a Hilbert space structure on a space of probability densities to project the infinite dimensional stochastic differential equation given by the filtering problem onto a finite dimensional manifold inside the space of densities. This reduces the problem to finite dimensional stochastic differential equation.Previously, the projection method has only been considered for the Hilbert space structure associated with the Hellinger metric. We show through the numerical example of the quadratic sensor that the approach also works well when one projects using the direct L 2 metric.Previous implementations of projection methods have been limited to solving a single problem. We indicate how one can build a computational framework for applying the projection method more generally.
Brigo D, Morini M, Pallavicini A, 2013, Counterparty Credit Risk, Collateral and Funding: with Pricing Cases for all Asset Classes, Publisher: Wiley, ISBN: 978-0-470-74846-6
The book’s content is focused on rigorous and advanced quantitative methods for the pricing and hedging of counterparty credit and funding risk. The new general theory that is required for this methodology is developed from scratch, leading to a consistent and comprehensive framework for counterparty credit and funding risk, inclusive of collateral, netting rules, possible debit valuation adjustments, re-hypothecation and closeout rules. The book however also looks at quite practical problems, linking particular models to particular ‘concrete’ financial situations across asset classes, including interest rates, FX, commodities, equity, credit itself, and the emerging asset class of longevity. The authors also aim to help quantitative analysts, traders, and anyone else needing to frame and price counterparty credit and funding risk, to develop a ‘feel’ for applying sophisticated mathematics and stochastic calculus to solve practical problems. The main models are illustrated from theoretical formulation to final implementation with calibration to market data, always keeping in mind the concrete questions being dealt with. The authors stress that each model is suited to different situations and products, pointing out that there does not exist a single model which is uniformly better than all the others, although the problems originated by counterparty credit and funding risk point in the direction of global valuation. Finally, proposals for restructuring counterparty credit risk, ranging from contingent credit default swaps to margin lending, are considered.
BRIGO D, CAPPONI A, PALLAVICINI A, et al., 2013, PRICING COUNTERPARTY RISK INCLUDING COLLATERALIZATION, NETTING RULES, RE-HYPOTHECATION AND WRONG-WAY RISK, International Journal of Theoretical and Applied Finance, Vol: 16, Pages: 1350007-1350007, ISSN: 0219-0249
<jats:p> This article is concerned with the arbitrage-free valuation of bilateral counterparty risk through stochastic dynamical models when collateral is included, with possible rehypothecation. The payout of claims is modified to account for collateral margining in agreement with International Swap and Derivatives Association (ISDA) documentation. The analysis is specialized to interest-rate and credit derivatives. In particular, credit default swaps are considered to show that a perfect collateralization cannot be achieved under default correlation. Interest rate and credit spread volatilities are fully accounted for, as is the impact of re-hypothecation, collateral margining frequency, and dependencies. </jats:p>
Brigo D, Morini M, Pallavicini A, 2013, Counterparty Credit Risk, Collateral and Funding <i>With Pricing Cases for All Asset Classes</i> Introduction, COUNTERPARTY CREDIT RISK, COLLATERAL AND FUNDING: WITH PRICING CASES FOR ALL ASSET CLASSES, Publisher: BLACKWELL SCIENCE PUBL, Pages: 3-+
Brigo D, Morini M, Pallavicini A, 2013, Modelling the Counterparty Default, COUNTERPARTY CREDIT RISK, COLLATERAL AND FUNDING: WITH PRICING CASES FOR ALL ASSET CLASSES, Publisher: BLACKWELL SCIENCE PUBL, Pages: 47-86
Brigo D, Morini M, Pallavicini A, 2013, Context, COUNTERPARTY CREDIT RISK, COLLATERAL AND FUNDING: WITH PRICING CASES FOR ALL ASSET CLASSES, Publisher: BLACKWELL SCIENCE PUBL, Pages: 31-45
Brigo D, Morini M, Pallavicini A, 2013, Wrong Way Risk (WWR) for Interest Rates, COUNTERPARTY CREDIT RISK, COLLATERAL AND FUNDING: WITH PRICING CASES FOR ALL ASSET CLASSES, Publisher: BLACKWELL SCIENCE PUBL, Pages: 121-134
Brigo D, Morini M, Pallavicini A, 2013, Unilateral CVA and Netting for Interest Rate Products, COUNTERPARTY CREDIT RISK, COLLATERAL AND FUNDING: WITH PRICING CASES FOR ALL ASSET CLASSES, Publisher: BLACKWELL SCIENCE PUBL, Pages: 89-120
Brigo D, Morini M, Pallavicini A, 2013, Conclusions and Further Work, COUNTERPARTY CREDIT RISK, COLLATERAL AND FUNDING: WITH PRICING CASES FOR ALL ASSET CLASSES, Publisher: BLACKWELL SCIENCE PUBL, Pages: 409-414
Brigo D, Morini M, Pallavicini A, 2013, Non-Standard Asset Classes: Longevity Risk, COUNTERPARTY CREDIT RISK, COLLATERAL AND FUNDING: WITH PRICING CASES FOR ALL ASSET CLASSES, Publisher: BLACKWELL SCIENCE PUBL, Pages: 385-408
Brigo D, Morini M, Pallavicini A, 2013, Funding Valuation Adjustment (FVA)?, COUNTERPARTY CREDIT RISK, COLLATERAL AND FUNDING: WITH PRICING CASES FOR ALL ASSET CLASSES, Publisher: BLACKWELL SCIENCE PUBL, Pages: 361-383
Brigo D, Morini M, Pallavicini A, 2013, Including Margining Costs in Collateralized Contracts, COUNTERPARTY CREDIT RISK, COLLATERAL AND FUNDING: WITH PRICING CASES FOR ALL ASSET CLASSES, Publisher: BLACKWELL SCIENCE PUBL, Pages: 351-359
Brigo D, Morini M, Pallavicini A, 2013, Bilateral Collateralized CVA and DVA for Rates and Credit, COUNTERPARTY CREDIT RISK, COLLATERAL AND FUNDING: WITH PRICING CASES FOR ALL ASSET CLASSES, Publisher: BLACKWELL SCIENCE PUBL, Pages: 331-350
Brigo D, Morini M, Pallavicini A, 2013, Bilateral CVA-DVA and Interest Rate Products, COUNTERPARTY CREDIT RISK, COLLATERAL AND FUNDING: WITH PRICING CASES FOR ALL ASSET CLASSES, Publisher: BLACKWELL SCIENCE PUBL, Pages: 279-303
Brigo D, Morini M, Pallavicini A, 2013, Close-Out and Contagion with Examples of a Simple Payoff, COUNTERPARTY CREDIT RISK, COLLATERAL AND FUNDING: WITH PRICING CASES FOR ALL ASSET CLASSES, Publisher: BLACKWELL SCIENCE PUBL, Pages: 319-330
Brigo D, Morini M, Pallavicini A, 2013, A First Attack on Funding Cost Modelling, COUNTERPARTY CREDIT RISK, COLLATERAL AND FUNDING: WITH PRICING CASES FOR ALL ASSET CLASSES, Publisher: BLACKWELL SCIENCE PUBL, Pages: 269-278
Brigo D, Morini M, Pallavicini A, 2013, Collateral, Netting, Close-Out and Re-Hypothecation, COUNTERPARTY CREDIT RISK, COLLATERAL AND FUNDING: WITH PRICING CASES FOR ALL ASSET CLASSES, Publisher: BLACKWELL SCIENCE PUBL, Pages: 305-317
Brigo D, Morini M, Pallavicini A, 2013, Unilateral CVA for FX, COUNTERPARTY CREDIT RISK, COLLATERAL AND FUNDING: WITH PRICING CASES FOR ALL ASSET CLASSES, Publisher: BLACKWELL SCIENCE PUBL, Pages: 205-244
Brigo D, Morini M, Pallavicini A, 2013, New Generation Counterparty and Funding Risk Pricing, COUNTERPARTY CREDIT RISK, COLLATERAL AND FUNDING: WITH PRICING CASES FOR ALL ASSET CLASSES, Publisher: BLACKWELL SCIENCE PUBL, Pages: 247-267
Brigo D, Morini M, Pallavicini A, 2013, Unilateral CVA for Equity with WWR, COUNTERPARTY CREDIT RISK, COLLATERAL AND FUNDING: WITH PRICING CASES FOR ALL ASSET CLASSES, Publisher: BLACKWELL SCIENCE PUBL, Pages: 167-203
Brigo D, Morini M, Pallavicini A, 2013, Unilateral CVA for Credit with WWR, COUNTERPARTY CREDIT RISK, COLLATERAL AND FUNDING: WITH PRICING CASES FOR ALL ASSET CLASSES, Publisher: BLACKWELL SCIENCE PUBL, Pages: 153-165
Brigo D, Morini M, Pallavicini A, 2013, Unilateral CVA for Commodities with WWR, COUNTERPARTY CREDIT RISK, COLLATERAL AND FUNDING: WITH PRICING CASES FOR ALL ASSET CLASSES, Publisher: BLACKWELL SCIENCE PUBL, Pages: 135-151
BRIGO D, BUESCU C, MORINI M, 2012, COUNTERPARTY RISK PRICING: IMPACT OF CLOSEOUT AND FIRST-TO-DEFAULT TIMES, International Journal of Theoretical and Applied Finance, Vol: 15, Pages: 1250039-1250039, ISSN: 0219-0249
<jats:p> In the absence of a universally accepted procedure for the credit valuation adjustment (CVA) calculation, we compare a number of different bilateral counterparty valuation adjustment (BVA) formulas. First we investigate the impact of the choice of the closeout convention used in the formulas. Important consequences on default contagion manifest themselves in a rather different way depending on which closeout formulation is used (risk-free or replacement), and on default dependence between the two entities in the deal. Second we compare the full bilateral formula with an approximation that is based on subtracting two unilateral credit valuation adjustment (UCVA) formulas. Although the latter might be attractive for its instantaneous implementation once one has a unilateral CVA system, it ignores the impact of the first-to-default time, when closeout procedures are ignited. We illustrate in a number of realistic cases both the contagion effect due to the closeout convention, and the CVA pricing error due to ignoring the first-to-default time. </jats:p>
Brigo D, Capproni A, 2012, Bilateral Credit Valuation Adjustment with Application to Credit Default Swaps, Managing and Measuring Capital: For Banks and Financial Institutions, Editors: Ong, Publisher: Risk Books
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