April 24, 2014

April 15-16, 2010 - Credit-Hybrid Risk

Talk Titles and Abstracts

Claudio Albanese
University of Toronto & Imperial College
Credit-equity models and High-Throughput Computing

It is possible to devise realistic structural credit-equity models that can be calibrated to the entire spectrum of credit-equity derivatives. Except that viable models are not analytically solvable and thus require a new type of mathematics and numerical analysis. Emerging multi-core microchip design make it possible to avoid entirely analytic solvability by evaluating transition probability kernels via third and fourth level BLAS. Dynamic copulas can then be evaluated either algebraically with dynamic conditioning or by Monte Carlo simulation. A combination of operator methods, high throughput linear algebra and Monte Carlo simulations executing on high density boards leads to a modelling framework that allows on to calibrate and price CDOs, hybrids and counterparty risk.

Claudio Albanese holds a PhD from ETH Zurich. He held regular faculty positions at the University of Toronto and Imperial College. He is currently Visiting Professor at King's College London and consults for various financial institutions.


Agostino Capponi
Ph.D, California Institute of Technology
Bilateral counterparty risk valuation with stochastic dynamical models and application to Credit Default Swaps

Authors: Damiano Brigo, Agostino Capponi

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) 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 Brigo and Chourdakis (2008), 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.

Short biography: Agostino Capponi received his Master and Ph.D Degree from the California Institute of Technology, respectively in 2006 and 2009. His research interests include credit risk modeling, counterparty risk valuation, stochastic filtering and recursive Bayesian estimation. He has published extensively in peer reviewed technical journals in the area of mathematical finance, system control and statistical signal processing. He has been an instructor of financial engineering in the D. Epstein Department of Industrial and Systems Engineering within the Viterbi School of Engineering at the University of Southern California from June 2009 to August 2009.


Giovanni Cesari
Managing Director, UBS
Modelling, Pricing, and Hedging Counterparty Credit Exposure

Building an accurate representation of firm-wide credit exposure, used for both trading and risk management, raises significant theoretical and technical challenges. In this talk we consider practical solutions to the problem of modelling, pricing, and hedging counterparty credit exposure for large portfolios of both vanilla and exotic derivatives. We start by presenting the main problems large Investment Banks face when computing counterparty exposure and we show how to define as generic modelling and valuation framework based on American Monte Carlo techniques. We describe how this modelling framework naturally leads to the definition of an architecture, which, with its modular design, allows the computation of credit exposure in a portfolio-aggregated and scenario-consistent way. An essential part of the design is the definition of a programming language, which allows trade representation based on dynamic modelling features. Finally we consider how to mitigate and hedge counterparty exposure. The crucial question of dynamic hedging is addressed by constructing a hybrid product, the Contingent-Credit Default Swap.

Short CV: Giovanni Cesari is Managing Director at UBS. He is the head of the portfolio-quant group, a front office team responsible for building models to compute and hedge counterparty credit exposure for the Investment Bank. Giovanni graduated from the University of Trieste and received his PhD from ETH in Zurich.

Other info:


Jean-Francois Chassagneux
Université Denis Diderot (P7)
Pricing Game Option using Reflected BSDEs

In this talk, we first present doubly reflected BSDEs with intermittent upper boundary and how they relate to the pricing and hedging of game option with possible 'call protection'.
We then propose a numerical scheme to approximate the solution of this particular type of reflected BSDEs and prove some convergence results for this scheme. Such numerical procedure appears to be an interesting alternative to PDE valuation techniques. Indeed, the PDE approach suffers generally the curse of dimensionality in the presence of 'call protection'. Our approach, based on Monte Carlo simulation, is very competitive in practice even for complicated 'call protection' clause.


Stephane Crepey
Evry University
CVA computation for counterparty risk assessment in credit portfolios (joint work with Samson Assefa, Tomasz R. Bielecki and Monique Jeanblanc)

We first derive representation formula for the Credit Value Adjustment (CVA) of a netted and collateralized portfolio. These results are This result is then specified to the case, most challenging from the modelling and numerical point of view, of counterparty credit risk. Our general results are essentially model free. Thus, although they are theoretically pleasing, they do not immediately lend themselves to any practical computations. We therefore subsequently introduce an underlying stochastic model, in order to to put the general results to work. We thus propose a Markovian model of portfolio credit risk in which dependence between defaults and the wrong way risk are represented by the possibility of simultaneous defaults among the underlying credit names. Specifically, single-name marginals in our model are themselves Markov, so that they can be pre-calibrated in the first stage, much like in the standard (static) copula approach. One can then calibrate the few model dependence parameters in the second stage. The numerical results show a good agreement of the behavior of EPE (Expected Positive Exposure) and CVA in the model with stylized features.

After a PhD Thesis in Applied Mathematics from Ecole Polytechnique at INRIA Sophia Antipolis and the Caisse Autonome de Refinancement (group `Caisse des Dépôts'), Stéphane Crépey is now an Associate Professor at the Mathematics Department of Evry University. He is director of the Master program MSC Financial Engineering of Evry University. His current research interests are Financial Modeling, Credit Risk, Numerical Finance, as well as connected mathematical topics in the fields of Backward Stochastic Differential Equations and PDEs.Stéphane Crépey also had various consulting activities in the banking and financial engineering sector.



Tom Hurd
Two factor models of equity and credit derivatives

We propose a simple extension of the structural credit modelling approach of Black and Cox to a unification of equity products (written on the stock price), and credit products like bonds and credit default swaps (CDS). Our models have two factors, which one might take to be log leverage and equity, whose dynamics are specified in terms of time-changed Brownian motions. They are capable of reproducing well known equity models such as the variance gamma model, at the same time producing the stylized facts about default stemming from structural models of credit.


Jan Kallsen
On the pricimg of game options and convertible bonds

In this talk we review some fundamental concepts for the valuation of game options in incomplete markets. This comprises static and dynamic approaches based on arbitrage and utility considerations. In any of these setups, the relation to Dynkin games plays a key role. As a special case we consider convertible bonds.

Short bio:
Jan Kallsen is professor at the university of Kiel (Germany) with specialisation in Mathematical Finance. He studied Mathematics and Physics in Kiel and Freiburg. He holds a PhD in Mathematics from Freiburg university. He spent extended research visits at Boston University and Technische Universität Wien. Prior to Kiel he held a position as associate professor at Technische Universität München. His primary research interest are financial mathematics and the theory of stochastic processes.

Yuri Kifer
Institute of Mathematics Hebrew University of Jerusalem Jerusalem, Israel
Perfect and Partial Hedging for Multiple Exercise (Swing) Game Options in Discrete And Continuous Time.

The work is joint with my PhD students Yan Dolinsky and Yonathan Iron.

The talk discusses hedging for game (Israeli) style extension of swing options in discrete and continuous time considered as multiple exercise derivatives. Assuming that the underlying security can be traded without restrictions we derive formulas for valuation of multiple exercise options via classical hedging arguments. Introducing the notion of the shortfall risk for such options we produce also partial hedging which leads to minimization of this risk in the discrete time case. Previous work of Carmona and Touzi and also of other authors dealt with multiple exercise options only as multiple opti- mal stopping problems without justifying fair prices of such options by hedging arguments. Hedging of multiple exercise options required new defnitions and the extension to the game options case involves, in particular, the study of multiple stopping Dynkin's games which, especially, in the continuous time case requires substantial additional work. There are natural situations not only in energy or commodity markets where multiple exercise options can be useful, for instance, when an investor wants to buy (or sell) a stock in several installments or when a producer plans to supply overseas his product in several shipments and, say, wants to ensure a favorable exchange rate at delivery times.


Rafael Mendoza-Arriaga
Time Changed Markov Processes in United Credit-equity Modeling

Hybrid credit-equity models are developed with state-dependent jumps, local- stochastic volatility and default intensity based on time changes of Markov processes. We model the stock price process as a time changed Markov process with state-dependent local volatility and killing rate. When the time change is a Levy process in turn time changed with a time integral of an activity rate process, the stock price process has state-dependent jumps, stochastic volatility and default intensity.

SHORT BIO. Rafael Mendoza-Arriaga is an assistant professor of Information, Risk and Operations Management at the University of Texas, McCombs School of Business. Dr. Mendoza received his doctorate in Industrial Engineering and Management Sciences from Northwestern University. He also holds a Master's degree in mathematical finance from the University of Toronto and in industrial engineering and management sciences from Northwestern University. Previously, he was a financial engineer at Algorithmics Inc. and a quantitative researcher at Citadel Group. Dr. Mendoza's industry experience includes the areas of market and credit risk, asset management and distributed computing. His research interests are on the application of analytical and computational methods for derivative security pricing based on spectral expansions and integral transforms. He has developed a credit-equity modeling framework based on time-changes of state dependent Markov processes with state dependent default hazard rates.

Abdhallah Rahal
Pricing Convertible Bonds with call protection

We consider the issue of pricing by simulation puttable and callable convertible bonds. Call times are typically subject to constraints, called call protections, that prevent the issuer from calling the bond during certain (random) time intervals. From the mathematical finance point of view, such bonds can be studied as certain type of game options with call protection. This leads to consideration of doubly reflected backward stochastic differential equations with an upper barrier, which is only active during random time intervals. A major practical concern is that call protection is typically monitored at discrete times, in a possibly very path-dependent way, which leads to highly-dimensional pricing problems.

We shall present certain recent results regarding valuation and hedging of convertible bonds subject to call protection and discrete time monitoring.


Dan Rosen
R2 Technologies
Pricing Counterparty Risk at the Trade Level and CVA Allocations

Joint work with Michael Pykhtin, Federal Reserve Bank

We address the problem of allocating the counterparty-level credit value adjustment (CVA) to the individual trades composing the portfolio. We show that this problem can be reduced to calculating contributions of the trades to the counterparty-level expected exposure (EE) conditional on the counterparty's default. We propose a methodology for calculating conditional EE contributions for both collateralized and non-collateralized counterparties. Calculation of EE contributions can be easily incorporated into exposure simulation processes, which already exist in a financial institution. We also derive closed-form expressions for EE contributions under the assumption that trade values are normally distributed. Analytical results are obtained for the case when the trade values and the counterparty's credit quality are independent as well as when there is a dependence between them (wrong-way risk).

Dan Rosen (bio) Dr. Dan Rosen is the CEO and co-founder of R2 Financial Technologies and acts as an advisor to institutions in Europe, North America, and Latin America on derivatives valuation, risk management, economic and regulatory capital. In addition, he is a visiting fellow at the Fields Institute for Research in Mathematical Sciences and an adjunct professor at the University of Toronto's Masters program in Mathematical Finance.

Dr. Rosen lectures extensively around the world on financial engineering, enterprise risk and capital management, credit risk and market risk. He has authored numerous papers on quantitative methods in risk management, applied mathematics, operations research, and has coauthored two books and various chapters in risk management books (including two chapters of PRMIA's Professional Risk Manger Handbook). In addition, Dr. Rosen is a member of the Industrial Advisory Boards of the Fields Institute and the Center for Advanced Financial Studies at the University of Waterloo, the Academic Advisory Board of Fitch, the Advisory Board, Educational and Credit Risk Steering Committees of the IAFE (International Association of Financial Engineers), the regional director in Toronto of PRMIA (Professional Risk Management International Association), and a member of the Oliver Wyman Institute. He is also one of the founders of RiskLab, an international network of research centers in Financial Engineering and Risk Management, initiated at the University of Toronto. Up to July 2005, Dr. Rosen had a successful ten-year career at Algorithmics Inc., where he held senior management roles in strategy and business development, research and financial engineering, and product marketing. In these roles, he was responsible for setting the strategic direction of its solutions, new initiatives and strategic alliances, as well as heading up the design and positioning of credit risk and capital management solutions, market risk management tools, operational risk, and advanced simulation and optimization techniques, as well as their application to several industrial settings. He holds an M.A.Sc. and Ph.D. in Chemical Engineering from the University of Toronto.


Julien Turc
Société Générale Corporate & Investment Banking
Joint modelling of credit spreads, share prices and volatility

This presentation adresses the structural and statistical relationships between the credit and equity markets. Both markets are naturally linked with each other, but understanding their relative valuation is far from easy. On the one hand, credit- equity relative value can be assessed through statistical analysis, with good results at the aggregated level. Adding dimensions greatly improves the efficiency of this approach, but one has to consider non linear features, crises and changes of regimes in particular. On the other hand, structural models provide an interesting insight at the company level. Stochastic calculus is particularly useful when it comes to jointly analysing credit and equity derivatives. Pricing shares and credit risk in a unified framework is a daunting task, with probably better results on high yield rather than investment grade companies.

Short Bio
Julien is head of Quantitative Research within the Cross-Asset Research group at Société Générale Corporate & Investment Banking.  The quantitative research team is active in global macro and relative value strategies, derivatives and structured products, and provides research to investors worldwide. Over the past 13 years, Julien's research has covered topics ranging from exotic credit derivatives pricing to statistical relative value and cross-asset strategies. Julien is a graduate of the Ecole Polytechnique and ENSAE and teaches credit derivatives at Paris VI University.