Publications
170 results found
Brigo D, Mercurio F, 2000, Option pricing impact of alternative continuous time dynamics for discretely observed stock prices, Finance and Stochastics, Vol: 4, Pages: 147-160
Brigo D, Hanzon B, Le Gland F, 1999, Approximate nonlinear filtering by projection on exponential manifolds of densities, BERNOULLI, Vol: 5, Pages: 495-534, ISSN: 1350-7265
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- Citations: 51
Brigo D, Mercurio F, 1999, Correction to: "Is Ito calculus oversold?", Risk Magazine, Vol: 12, Pages: 67-67
Brigo D, 1999, Diffusion Processes, Manifolds of Exponential Densities, and Nonlinear Filtering, Geometry in Present Day Science, Editors: Barndorff-Nielsen, Jensen, Publisher: World Scientific
Brigo D, Hanzon B, 1998, On some filtering problems arising in mathematical finance, International Workshop on the Interplay between Insurance, Finance and Control, Publisher: ELSEVIER SCIENCE BV, Pages: 53-64, ISSN: 0167-6687
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- Citations: 18
Brigo D, Hanzon B, LeGland F, 1998, A differential geometric approach to nonlinear filtering: The projection filter, IEEE TRANSACTIONS ON AUTOMATIC CONTROL, Vol: 43, Pages: 247-252, ISSN: 0018-9286
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- Citations: 54
Brigo D, Hanzon B, 1998, On some filtering problems arising in mathematical finance, Insurance: Mathematics and Economics, Vol: 22, Pages: 53-64
Brigo D, LeGland F, 1997, A finite dimensional filter with exponential conditional density, 36th IEEE Conference on Decision and Control, Publisher: IEEE, Pages: 1643-1644, ISSN: 0191-2216
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- Citations: 2
Brigo D, 1997, On nonlinear SDE's whose densities evolve in a finite dimensional family, Stochastic Differential and Difference Equations, Editors: Csiszar, Michaletzky, Publisher: Birkhauser
Brigo D, 1996, New results on the Gaussian protection filter with small observation noise, SYSTEMS & CONTROL LETTERS, Vol: 28, Pages: 273-279, ISSN: 0167-6911
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- Citations: 3
Brigo D, 1995, On the nice behaviour of the Gaussian projection filter with small observation noise, SYSTEMS & CONTROL LETTERS, Vol: 26, Pages: 363-370, ISSN: 0167-6911
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- Citations: 7
Brigo D, Hanzon B, LeGland F, 1995, A differential geometric approach to nonlinear filtering: The projection filter, 34th IEEE Conference on Decision and Control, Publisher: I E E E, Pages: 4006-4011
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- Citations: 6
Brigo D, El-Bachir N, An exact formula for default swaptions' pricing in the SSRJD stochastic intensity model
We develop and test a fast and accurate semi-analytical formula for single-name default swaptions in the context of a shifted square root jump diffusion (SSRJD) default intensity model. The model can be calibrated to the CDS term structure and a few default swaptions, to price and hedge other credit derivatives consistently. We show with numerical experiments that the model implies plausible volatility smiles.
Brigo D, El-Bachir N, Credit Derivatives Pricing with a Smile-Extended Jump Stochastic Intensity Model
We present a two-factor stochastic default intensity and interest rate model for pricing single-name default swaptions. The specific positive square root processes considered fall in the relatively tractable class of affine jump diffusions while allowing for inclusion of stochastic volatility and jumps in default swap spreads. The parameters of the short rate dynamics are first calibrated to the interest rates markets, before calibrating separately the default intensity model to credit derivatives market data. A few variants of the model are calibrated in turn to market data, and different calibration procedures are compared. Numerical experiments show that the calibrated model can generate plausible volatility smiles. Hence, the model can be calibrated to a default swap term structure and few default swaptions, and the calibrated parameters can be used to value consistently other default swaptions (different strikes and maturities, or more complex structures) on the same credit reference name.
Bellotti A, Brigo D, Gambetti P, et al., Forecasting Recovery Rates on Non-Performing Loans with Machine Learning, Publisher: Elsevier BV
El-Bachir N, Brigo D, An analytically tractable time-changed jump-diffusion default intensity model
We present a stochastic default intensity model where the intensity follows a tractable jump-diffusion process obtained by applying a deterministic change of time to a non mean-reverting square root jump-diffusion process. The model generates higher implied volatilities for default swaptions than mean-reverting versions, consistent with volatility levels observed on the market.
Brigo D, Predescu M, Capponi A, Credit Default Swaps Liquidity modeling: A survey
We review different approaches for measuring the impact of liquidity on CDS prices. We start with reduced form models incorporating liquidity as an additional discount rate. We review Chen, Fabozzi and Sverdlove (2008) and Buhler and Trapp (2006, 2008), adopting different assumptions on how liquidity rates enter the CDS premium rate formula, about the dynamics of liquidity rate processes and about the credit-liquidity correlation. Buhler and Trapp (2008) provides the most general and realistic framework, incorporating correlation between liquidity and credit, liquidity spillover effects between bonds and CDS contracts and asymmetric liquidity effects on the Bid and Ask CDS premium rates. We then discuss the Bongaerts, De Jong and Driessen (2009) study which derives an equilibrium asset pricing model incorporating liquidity effects. Findings include that both expected illiquidity and liquidity risk have a statistically significant impact on expected CDS returns. We finalize our review with a discussion of Predescu et al (2009), which analyzes also data in-crisis. This is a statistical model that associates an ordinal liquidity score with each CDS reference entity and allows one to compare liquidity of over 2400 reference entities. This study points out that credit and illiquidity are correlated, with a smile pattern. All these studies highlight that CDS premium rates are not pure measures of credit risk. Further research is needed to measure liquidity premium at CDS contract level and to disentangle liquidity from credit effectively.
Brigo D, Pallavicini A, Torresetti R, Credit models and the crisis: default cluster dynamics and the generalized Poisson loss model, JOURNAL OF CREDIT RISK, Vol: 6, Pages: 39-81, ISSN: 1744-6619
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- Citations: 7
Brigo D, Capponi A, Bilateral counterparty risk valuation with stochastic dynamical models and application to Credit Default Swaps
We introduce the general arbitrage-free valuation framework for counterparty risk adjustments in presence of bilateral default risk, including default of the investor. We illustrate the symmetry in the valuation and show that the adjustment involves a long position in a put option plus a short position in a call option, both with zero strike and written on the residual net value of the contract at the relevant default times. We allow for correlation between the default times of the investor, counterparty and underlying portfolio risk factors. We use arbitrage-free stochastic dynamical models. We then specialize our analysis to Credit Default Swaps (CDS) as underlying portfolio, generalizing the work of Brigo and Chourdakis (2008) [5] who deal with unilateral and asymmetric counterparty risk. We introduce stochastic intensity models and a trivariate copula function on the default times exponential variables to model default dependence. Similarly to [5], we find that both default correlation and credit spread volatilities have a relevant and structured impact on the adjustment. Differently from [5], the two parties will now agree on the credit valuation adjustment. We study a case involving British Airways, Lehman Brothers and Royal Dutch Shell, illustrating the bilateral adjustments in concrete crisis situations.
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