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.
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Agostino Capponi
Ph.D, California Institute of Technology
www.cs.caltech.edu/~acapponi
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.
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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:
http://www.springer.com/math/quantitative+finance/book/978-3-642-04453-3
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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.
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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.
Bio:
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.
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Tom Hurd
McMaster
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.
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Jan Kallsen
kallsen@math.uni-kiel.de
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.
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Yuri Kifer
Institute of Mathematics Hebrew University of Jerusalem Jerusalem,
Israel
www.math.huji.ac.il/~kifer
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.
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Rafael Mendoza-Arriaga
UTexas
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.
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Abdhallah Rahal
Bank AUDI
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.
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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.
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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.
