
20082009
Seminar Series on Quantitative Finance
held at the Fields Institute, 222 College St., Toronto
sponsored by


The Quantitative
Finance Seminar has been a centerpiece of the Commercial/Industrial
program at the Fields Institute since 1995. Its mandate is to arrange
talks on current research in quantitative finance that will be of
interest to those who work on the border of industry and academia.
Wide participation has been the norm with representation from mathematics,
statistics, computer science, economics, econometrics, finance and
operations research. Topics have included derivatives valuation, credit
risk, insurance and portfolio optimization. Talks occur on the last
Wednesday of every month throughout the academic year and start at
5 pm. Each seminar is organized around a single theme with two 45minute
talks and a half hour reception. There is no cost to attend these
seminars and everyone is welcome.
To be informed of speakers and titles for upcoming seminars and
financial mathematics activities, please subscribe to the Fields
mail list.
Seminars
200809 
April 29, 2009 
Andrew W. Lo, Director, MIT Laboratory for Financial
Engineering, MIT Sloan School of Management
"Kill All The Quants"?: Models vs. Mania In The
Current Financial Crisis
Audio of talk
As the shockwaves of the financial crisis of 2008 propagate
throughout the global economy, the "blame game"
has begun in earnest, with some fingers pointing to the complexity
of certain financial securities, and the mathematical models
used to manage them. In this talk, I will review the evidence
for and against this perspective, and argue that a broader
perspective will show a much different picture. Blaming quantitative
analysis for the financial crisis is akin to blaming F = MA
for a fallen mountain climber's death. Instead, we need to
look deeper into the underlying causes of financial crisis,
which ultimately leads to the conclusion that bubbles, crashes,
and market dislocation are unavoidable consequences of hardwired
human behavior coupled with free markets and modern capitalism.
However, even though crises cannot be legislated away, there
are many ways to reduce the disruptive effects of these events,
and I will conclude with a set of proposals for regulatory
reform.
and
Lane Hughston, Imperial College London
Information Flows in Financial Markets
(audio and slides)
What causes price changes in financial assets? Clearly, one
of the major determiners of price changes is "new information".
When a new piece of information circulates in a financial
market (whether true, partly true, misleading, or bogus),
the prices of related assets will typically be adjusted in
response by market participants, and will move again when
the information is updated. The role of information is evident
enough on an intuitive basis, but how do we
model this mathematically? What is the information "about"?
In this talk I indicate some of the issues involved in modeling
"the flow of information" in financial markets,
and I present some elementary and very useful mathematical
models for "information" in various situations.
Informationbased models for a number of different types of
asset price processes will be reviewed, and applications to
the pricing of certain types of derivative products will be
indicated.
Finally, I discuss theproblem of "price formation"
in markets involving interacting agents with diverse, heterogeneous
information sources. [Based on work carried out in collaboration
with D. Brody, A. Macrina, E. Hoyle, and others.]

April 1, 2009
Please Note Date Change 
Audio and Slides
of the talk
Helyette Geman, School of Economics, Mathematics
and Statistics, Birkbeck, University of London
Inventory, Scarcity and Price Volatility in Oil and Natural
Gas Markets
The role of inventory in explaining the shape of the forward
curve and spot price volatility in commodity markets is central
in the theory of storage developed by Kaldor (1939) and Working
(1949) and has since been documented in a vast body of financial
literature, including the reference paper by Fama and French
(1987) on metals.
The goal of this paper is twofold: i) validate in the case
of oil and natural gas the use of the slope of the forward
curve as a proxy for inventory (the slope being defined in
a way that filters out seasonality); ii) analyze directly
for these two major commodities the relationship between inventory
and price volatility. In agreement with the theory of storage,
we find that:
i) the negative correlation between price volatility and inventory
is globally significant for crude oil;
ii) this negative correlation prevails only during those periods
of scarcity when the inventory is below the historical average
and increases importantly during the winter periods for natural
gas. Our results are illustrated by the analysis of a 15 yeardatabase
of US oil and natural gas prices and inventory.
The talk will start with a discussion of the dramatic moves
in commodity prices over the last 10 years.
and
Erhan Bayraktar, Department of Mathematics, University
of Michigan
A Unified Framework for Pricing Credit and Equity Derivatives
We propose a model which can be jointly calibrated to
the corporate bond term structure and equity option volatility
surface of the same company. Our purpose is to obtain explicit
bond and equity option pricing formulas that can be calibrated
to find a risk neutral model that matches a set of observed
market prices. This risk neutral model can then be used to
price more exotic, illiquid or overthecounter derivatives.
We observe that the model implied credit default swap (CDS)
spread matches the market CDS spread and that our model produces
a very desirable CDS spread term structure. This is observation
is worth noticing since without calibrating any parameter
to the CDS spread data, it is matched by the CDS spread that
our model generates using the available information from the
equity options and corporate bond markets. We also observe
that our model matches the equity option implied volatility
surface well since we properly account for the default risk
premium in the implied volatility surface. We demonstrate
the importance of accounting for the default risk and stochastic
interest rate in equity option pricing by comparing our results
to Fouque, Papanicolaou, Sircar and Solna (2003), which only
accounts for stochastic volatility.
Joint work with my former Ph.D. student Bo Yang (now at Morgan
Stanley).

February 25,
2009

Audio and Slides
of the talk
Michael Pykhtin, Bank of America
Modeling Credit Exposure for Collateralized Counterparties
Modeling credit exposure of a financial institution to
a counterparty usually requires Monte Carlo simulation of
the trade values at future time points. For collateralized
counterparties, collateral at any simulation time point depends
on the portfolio value at an earlier time point because of
the margin period of risk. Thus, to simulate collateralized
exposure at a single (primary) time point, one needs to simulate
the trade values at two time points: primary and look back,
resulting in doubling of the total simulation time.
In this talk, we present a method for calculating expected
exposure profile for collateralized counterparties that does
not require simulating trade values at the lookback time
points. This method can be easily implemented within an existing
system that simulates uncollateralized exposure without a
noticeable increase of the simulation time. Potential applications
of the method include pricing and hedging of counterparty
credit risk and calculating economic and
regulatory capital.
and
Adam Metzler, University of Western Ontario
A Multiname First Passage Model for Credit Risk
In this talk we investigate a general framework for multiname
first passage models in credit risk. We begin with a brief
overview of the seminal BlackCox model for corporate defaults.
In multiname extensions of this model, dependence between
defaults is typically introduced by correlating the Brownian
motions driving firm values. Despite its significant intuitive
appeal, such a framework is simply not capable of describing
market data. Our suspicion is that the ``location’’
of systematic risk here is the model’s fatal flaw.
In the remainder of the talk we discuss an alternative framework,
obtained by ``altering’’ the location of systematic
risk in the Black Cox model. This is accomplished by introducing
``systematic risk’’ processes, which govern the
trend and volatility in obligors’ credit qualities. The
result is a setting where defaults occur upon first passage
of timechanged Brownian motion to stochastic barriers. By
exploiting a conditional independence structure we are able
to
calibrate several versions of the model to market quotes for
CDX index tranches, including quotes from the current distressed
environment.

January 28, 2009 
"CANCELLED"

November 26, 2008 
5:00 p.m.  Reception
5:30 p.m.Audio and
Slides of the talk
Stathis Tompaidis, IROM Department, and Department
of Finance, McCombs School of Business
University of Texas at Austin
The Impact of Financial Constraints on Individual Asset
Allocations: Underdiversification and Asset Selection
We offer a rational explanation for the observed underdiversification
of household portfolios in a partial equilibrium setting with
an investor with a constant investment opportunity set that
includes multiple risky assets, and who receives an income
stream and faces financial constraints. We develop a numerical,
simulationbased, algorithm for estimating the optimal portfolio
weights and apply it to 5 industry portfolios. We find that
young investors with relatively few financial assets compared
to their income, choose portfolios that are concentrated in
one or two assets, while investors closer to retirement revert
back to holding portfolios with all the assets available.
We also consider general equilibrium crosssectional implications
of financial constraints in an overlappinggenerations model
and discuss the potential of financial constraints in explaining
observed deviations from the predictions of the Capital Asset
Pricing Model.

October 29, 2008 
Audio and Slides
of the talks
Dr. Michael Zerbs, Algorithmics
Credit Risk Management  The Next Wave
Best practice in credit risk management will continue
to evolve rapidly, in response to ongoing innovation and current
market dislocations. To enable effective risk aware business
decisions at the operational and strategic level, it is more
important than ever to have a sound conceptual framework,
the comprehensive coverage of interrelated risks and asset
or liability classes, flexibility in modeling choices. A forward
looking perspective will be offered on credit risk management,
major objectives and resulting requirements.
Mark Broadie, Columbia University
Understanding Index Option Returns
Previous research concludes that options are mispriced based
on the high average returns, CAPM alphas, and Sharpe ratios
of various put selling strategies. One criticism of these
conclusions is that these benchmarks are illsuited to handle
the extreme statistical nature of option returns generated
by nonlinear payoffs. We propose an alternative way to evaluate
statistical significance of option returns by comparing historical
statistics to those generated by wellaccepted option pricing
models. The most puzzling finding in the existing literature,
the large returns to writing outofthemoney puts, are not
inconsistent (i.e., are statistically insignificant) relative
to the BlackScholes model or the Heston stochastic volatility
model due to the extreme sampling uncertainty associated with
put returns. This sampling problem can largely be alleviated
by analyzing marketneutral portfolios such as straddles or
deltahedged returns. The returns on these portfolios can
be explained by jump risk premia and estimation risk.

September 24, 2008 
Audio and
Slides of the talk
William Morokoff, Standard and Poor's
Modeling Correlation in Credit Risk Management
Effective credit risk management depends on a proper estimation
of the distribution of future losses for a portfolio of credit
risky securities. Due to the limited upside of credit assets,
but substantial downside due to relatively rare events of
default, credit portfolios display strong asymmetry in the
shape of fat tails. Correlation, in the form of joint dependencies
in credit movements of the constituent portfolio assets, is
therefore a critical driver of credit risk since it directly
defines the fat tails of the loss distribution and prevents
full diversification of the credit portfolio. Researchers
and risk management practitioners have thus increasingly turned
towards better understanding and properly estimating credit
correlations. Somewhat in parallel, the past decade has also
witnessed the growth of securities such as CDOs that allow
market participants to directly trade credit correlations.
The talk will provide an overview of the different approaches
to modeling dependencies in credit evolutions such as top
down vs bottom up methods, structural models for pricing (based
on a forward looking, risk neutral measure) and risk management
(calibrated to historical, physical measure), estimation of
correlation from market data such as equity prices, spreads
on credit derivatives or observance of credit events such
as defaults and rating migrations. Some thoughts will also
be provided on the challenges related to credit correlation
estimation due to the paucity of default events, and to a
lesser extent, credit migration data. The impact of model
assumptions used to link correlations estimated from high
frequency or multiperiod data to long horizon loss distributions
(typically one year for economic capital calculations and
longer term for ratings analyses) will also be discussed.

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