
20102011
Fields Quantitative Finance Seminar
Fields Institute, 222 College St., Toronto

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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
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Seminars 20102011






April 27, 2011
5:00 p.m.
Audio
&
Slides of the Talks 
Xunyu Zhou (Oxford University)
Behavioural Portfolio Choice
I will first give a brief introduction on the motivation
and background of behavioural finance theory, and then present
an overview of the recent development on quantitative treatment
of behavioural finance, primarily in the setting of portfolio
choice under the cumulative prospect theory. Financial motivations
and methodological challenges of the problem are highlighted.
It is demonstrated that the solutions to the problem have
in turn led to new financial and mathematical problems and
machinery.
and
Patrick Cheridito
Pricing and Hedging in Affine Models with Possibility
of Default
We propose a general class of models for the simultaneous
treatment of equity, corporate bonds, government bonds and
derivatives. The noise is generated by a general affine Markov
process. The framework allows for stochastic volatility, jumps,
the possibility of default and correlations between different
assets. We extend the notion of a discounted moment generation
function of the log stock price to the case where the underlying
can default and show how to calculate it in terms of a coupled
system of generalized Riccati equations. This yields an efficient
method to compute prices of power payoffs and Fourier transforms.
European calls and puts as well as binaries and assetornothing
options can then be priced with the fast Fourier transform
methods of Carr and Madan (1999) and Lee (2005). Other European
payoffs can be approximated by a linear combination of power
payoffs and vanilla options. We show the results to be superior
to using only power payoffs or vanilla options. We also give
conditions for our models to be complete if enough financial
instruments are liquidly tradable and study dynamic hedging
strategies. As an example we discuss a Hestontype stochastic
volatility model with possibility of default and stochastic
interest rates. Joint work with Alexander Wugalter.

March
30, 2011
5:00 p.m.
Audio
&
Slides of the Talks 
Rafael MendozaArriaga (The University of Texas at
Austin)
Constructing Markov Processes with Dependent Jumps
by Multivariate Subordination: Applications to MultiName
CreditEquity Modeling
We develop a new class of multiname unified creditequity
models that jointly model the stock prices of multiple firms,
as well as their default events, by a multidimensional Markov
semimartingale constructed by multivariate subordination of
jumptodefault extended constant elasticity of variance (JDCEV)
diffusions. Each of the stock prices experiences statedependent
jumps with the leverage effect (arrival rates of large jumps
increase as the stock price falls), including the possibility
of a jump to zero (jump to default). Some of the jumps are
idiosyncratic to each firm, while some are either common to
all firms (systematic), or common to a subgroup of firms.
For the twofirm case, we obtain analytical solutions for
credit derivatives and equity derivatives, such as basket
options, in terms of eigenfunction expansions associated with
the relevant subordinated semigroups.
*****************
Alfred Lehar (University of Calgary)
Macroprudential capital requirements and systemic risk
Full Paper Available Here
When regulating banks based on their contribution to the overall
risk of the banking system we have to consider that the risk
of the banking system as well as each bank’s risk contribution
changes once bank equity capital gets reallocated. We define
macroprudential capital requirements as the fixed point at
which each bank’s capital requirement equals its contribution
to the risk of the system under the proposed capital requirements.
This study uses two alternative models, a network based framework
and a Merton model, to measure systemic risk and how it changes
with bank capital and allocates risk to individual banks based
on fi;ve risk allocation mechanisms used in the literature.
Using a sample of Canadian banks we find that macroprudential
capital allocations can differ by as much as 70% from observed
capital levels, are not trivially related to bank size or
individual bank default prob ability, increase in interbank
assets, and differ substantially from a simple risk attribution
analysis. We further find that across both models and all
risk allocation mechanisms that macroprudential capital requirements
reduce the default probabilities of individual banks as well
as the probability of a systemic crisis by about 25%. Macroprudential
capital requirements are robust to model risk and are positively
correlated to future capital raised by banks as well as future
losses in equity value. Our results suggest that financial
stability can be substantially enhanced by implementing a
systemic perspective on bank regulation.

Feb. 23, 2011
Room 230, 5pm
Audio
&
Slides of the Talks 
Mike
Ludkovski (UCSB)
Price Discrepancies and Optimal Timing to Buy Options
In incomplete markets, where not all risks can be hedged, different
riskneutral or riskaverse pricing models may yield a range
of noarbitrage prices. Consequently, the investor's model price
may disagree with the market price. This leads to the natural
and important question of when is the optimal time to buy a
derivative security from the market. In this talk, I will discuss
an investor who attempts to maximize the spread between her
model price and the offered market price through optimally timing
the purchase. Both the investor and the market value the options
by riskneutral expectations but under different equivalent
martingale measures representing different market views or risk
premia specifications. We show that the structure of the resulting
optimal stopping problem depends on the interaction between
the respective market price of risk and the option payoff. In
particular, a crucial role is played by the delayed purchase
premium that is related to the stochastic bracket between the
market price and the buyer' risk premia. Explicit characterization
of the purchase timing is given for two representative classes
of Markovian models: (i) defaultable equity models with local
intensity; (ii) diffusion stochastic volatility models. I will
conclude with several numerical examples to illustrate the results
and ongoing work on extensions to riskaverse agents.
This is joint work with Tim Leung (Johns Hopkins).

Nov. 24, 2010
Room 230, 5pm
Audio
&
Slides of the Talks 
Pierre CollinDufresne (Carson Family Professor of
Finance, Columbia University)
On the Relative Pricing of long Maturity S&P 500 Index
Options and CDX Tranches
We investigate a structural model of market and firmlevel
dynamics in order to jointly price longdated S&P 500
options and tranche spreads on the fiveyear CDX index. We
demonstrate the importance of calibrating the model to match
the entire term structure of CDX index spreads because it
contains pertinent information regarding the timing of expected
defaults and the specification of idiosyncratic dynamics.
Our model matches the time series of tranche spreads well,
both before and during the financial crisis, thus offering
a resolution to the puzzle reported by Coval, Jurek and Stafford
(2009).
*****************
Kostas Kardaras (Boston University)
Pricing and hedging barrier options in diffusion models
via 3dimensional Bessel bridges
Due to the discontinuous payoff of barrier options, finite
difference methods typically lead to large error for the price
function and spatial derivatives near expiry date and the
barrier. Furthermore, usual MonteCarlo estimators for their
price and sensitivities typically have significant variance.
In this work, we consider alternative representations for
barrier option prices in terms of the 3dimensional Bessel
bridge, and show how this leads to better estimators, especially
for short maturities where we are able to increase the estimator
efficiency dramatically.
We also discuss the related problem of efficient estimation
of the density of firstpassage times for diffusions. Even
though the density estimation problem is essentially nonparametric,
our method achieves (the typical MonteCarlo) squareroot
order of convergence.

Oct. 27, 2010
Room 230, 5pm
Audio
&
Slides of the Talks 
Fernando Zapatero (Marshall School of Business, University
of Southern California)
Executive Stock Options as a Screening Mechanism
Coauthors: Abel Cadenillas (Department of Mathematical and
Statistical Sciences, University of Alberta) & Jaksa Cvitanic
(Division of Humanities and Social Sciences, Caltech)
We study how and when option grants can be the optimal compensation
to screen lowability executives. In a dynamic setting, we
consider the problem of a riskneutral firm that tries to
hire a riskaverse executive whose actions can affect the
expected return and volatility of the stock price. Even if
the optimal compensation for all types of executives is stock
under complete information, it might be optimal to offer options
under incomplete information. We show that the likelihood
of using options increases with the dispersion of types and
the size of the firm, and decreases with the availability
of growth opportunities for the firm.
*****************
Emanuel Derman (Columbia University)
Metaphors, Models & Theories in Science and Finance
There has been a great deal of confusion about the role of
models in the financial crisis. In this talk I want to discuss
the possible ways of describing and explaining the world.
Scientific theories deal with the natural world on its own
terms, and can achieve great truth and accuracy. They are
very rare. Models in finance are not theories; they are closer
to metaphors that try to describe the object of their attention
by comparing it to something else they already understand
via theories. Models are idealizations that always sweep dirt
under the rug, and good models tell you what kind of dirt
it is, and where it lies.

Sept. 29, 2010
Room 230, 5pm
Audio
&
Slides of the Talks

Liuren Wu (Professor of Economics and Finance, Zicklin
School of Business, Baruch College)
A New Approach to Constructing Implied Volatility Surfaces
Coauthors: Peter Carr
Standard option pricing often specifies the dynamics of the
security price and the instantaneous variance rate, and derives
its noarbitrage implication for the option implied volatility
surface. Market models have also been proposed to start with
an initial implied volatility surface and a diffusion specification
for the implied volatility dynamics, and derive the noarbitrage
constraints on the riskneutral drift of the dynamics. This
paper proposes a new approach, which specifies the security
price dynamics, but leaves the instantaneous variance rate
dynamics unspecified while specifying implied volatility dynamics
instead. The allowable shape for the initial implied volatility
surface is then derived based on dynamic noarbitrage arguments.
Two parametric specifications for the implied volatility dynamics
lead to particularly tractable solutions for the whole implied
volatility surface, as the surface can be represented as solutions
to simple quadratic equations. The paper also proposes a dynamic
calibration methodology and calibrates the two models to overthecounter
currency option and equity index option implied volatility
surfaces over an 11year period. The pricing performance is
similar to standard option pricing models of similar complexities,
but calibrating them is 100 times faster.
*****************
Alexey Kuznetsov (York University)
Meromorphic Levy processes and their applications in Finance
and Insurance
What is the distribution of the first passage time of the
Variance Gamma process? What is the price of the double barrier
option in the CGMY model? How can I compute the GerberShiu
function for
something more interesting than a compound Poisson process
with exponential jumps? We all know that these are very hard
questions, and despite a multitude of research papers published
in this area there is still no consensus on what are the right
answers. So if we can't find the answer, let's modify the
question: can we find an interesting and large enough class
of Levy processes for which all these problems can be solved?
In this talk we will answer this last question in the affirmative
by introducing meromorphic Levy processes. This is joint work
with A.E.Kyprianou (University of Bath, UK), M.Morales (University
of Montreal, Canada) and J.C.Pardo (CIMAT, Mexico).

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