
THE FIELDS
INSTITUTE
FOR RESEARCH IN MATHEMATICAL SCIENCES 
20112012
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 and financial
mathematics activities, please subscribe to the Fields mail
list.
Wed. April 25, 2012
5:00 p.m.
Fields Institute,
Room 230 
Rogemar
Mamon, University of Western Ontario
A weak hidden Markov chainmodulated model for asset allocation
A discretetime weak hidden Markov model (WHMM) is proposed
to capture both the switching of economic regimes and memory
property of time series data. The drifts and volatilities
of asset returns switch over time according to the WHMM dynamics.
A multivariate filtering technique in conjunction with the
ExpectationMaximisation algorithm is developed to obtain
estimates of model parameters. An analysis of ``switching"
and "mixed" strategies in asset allocation is presented.
The use of financial signal processing via filtering aids
investors in determining the optimal investment strategy for
the next time step. Numerical implementation is carried out
on the datasets of Russell 3000 value and growth indices.
We benchmark portfolio performances using three classical
investment measures.
Joint work with:
Matt Davison (Departments of Applied Mathematics, Statistical
& Actuarial Sciences, and Richard Ivey School of Business,
UWO) and Jean Xi (Department of Applied Mathematics, UWO)
====================================
Steve Shreve, Carnegie Mellon University
Optimal Execution in a General OneSided Limit Order Book
We construct an optimal execution strategy for the purchase
of a large number of shares of a financial asset over a fixed
interval of time. Purchases of the asset have a nonlinear
impact
on price, and this is moderated over time by resilience in
the limitorder book that determines the price. The limitorder
book is permitted to have arbitrary shape. The form of the
optimal execution strategy is to make an initial lump purchase
and then purchase continuously for some period of time during
which the rate of purchase is set to match the order book
resiliency. At the end of this period, another lump purchase
is made, and following that there is again a period of purchasing
continuously at a rate set to match the order book resiliency.
At the end
of this second period, there is a final lump purchase. Any
of the lump purchases could be of size zero. A simple condition
is provided that guarantees that the intermediate lump purchase
is of size zero. This is joint work with Gennady Shaikhet
and Silviu Predoiu.

Wed. March 28, 2012
5:00 p.m.
Fields Institute,
Room 230 
Abel Cadenillas, Mathematics, University of Alberta
A Theory for the Optimal Government Debt Control
Motivated by the current debt crisis in the world, we consider
a government that wants to end the optimal control of its
debt ratio. The debt generates a cost for the country. The
government can reduce the debt ratio, but there is a cost
associated with this reduction. We obtain a solution for the
government debt problem. This is joint work with Ricardo Huaman.
====================================
**Paul Embrechts, Mathematics,
ETH Zurich
Four Theorems and a Financial Crisis
In this talk I will give my personal assessment of the
financial crisis (crises) and discuss where quantitative risk
management (QRM) went wrong. I will formulate four mathematical
theorems/research areas which have relevance for financial
crises in general. Related to these theorems, key issues to
be discussed are:
1) financial alchemy on Wall street
2) risk measurement for catastrophic risks
3) clustering of extremal events, and
4) beware of linear correlation.
** Note Tuesday, March 27, 2012
Paul Embrechts, will be speaking at McMaster University
Venue: 15:30  16:30 in Hamilton Hall 109, McMaster University
The Financial Crisis as a Crisis of Financial Mathematics?

Wed. March 7, 2012**
5:00 p.m.
Fields Institute,
Room 230
Lecture Notes
***Please note the change in date

Alex Levin, Director, Methodology, Market &
Trading Credit Risk, RBC Financial Group
Some Approaches to Modeling WrongWay Risk in Counterparty
Credit Risk Management and CVA
Current Risk Management methods focus on Credit Value
Adjustment (CVA) for pricing credit risk of derivative portfolios
and Counterparty Credit Risk (CCR) measurement, and are especially
concerned with issues related to modeling WrongWay Risk (WWR)
 dangerous positive correlation between the exposure to a
counterparty and its default probability. In this talk, we
will explore several new Counterparty Credit Risk measures
that account well for WrongWay Risk and RightWay Risk. I
will then introduce a multifactor "Gaussian  jump of
arbitrary sign" default intensity framework for modeling
Wrong/RightWay Risk and credit rating transitions (credit
triggers) for large derivative portfolios with thousands of
counterparties with or without collateral agreements. We will
look at some calibration examples of this model, following
a procedure based on a Volterra integral equation for the
hitting time distributions. We will develop a sufficiently
general Monte Carlo simulation algorithm for model calibration
based on the idea of sequential fitting the drift to a term
structure of CDS spreads. Finally, I will describe a new approach
to Portfolio CCR and bilateral CVA calculations we call the
"GammaFactor Copula".

Wed. January 25, 2012
5:00 p.m.

Bruno Dupire, Head of Quantitative Research, Bloomberg
Functional Ito Calculus and Risk Management
We introduce the Functional Ito Calculus, which gives
a natural setting for defining the Greeks for path dependent
options and gives a generalized PDE for the price of path
dependent options, even in the case of non Markov dynamics.
It leads to a variational calculus on volatility surfaces
and a fine decomposition of the volatility risk as well to
links with superreplication strategies. We examine a few
practical examples and analyze the ability to hedge (or not)
some popular structures.

Wed. Nov 16, 2011
5:00 p.m.

Peter Carr, Morgan Stanley
Optionality and Volatility
We propose two new concepts in option pricing called optionality
and money vol. We provide financial interpetations of each
in the context of various models.
We show how money vol can be used to generate dynamics for
the underlying which is consistent with a given smile.
=================
Alexander Lipton, Bank of America
Filling the Gaps
The calibration of local volatility models to market data
is one of the most fundamental problems of financial engineering.
Under the restrictive assumption that the entire implied volatility
surface is known, this problem can be solved by virtue of
the socalled Dupire equation. In reality, however, the number
of available data points is very limited and construction
of a nonarbitrageable implied volatility surface is difficult,
if not impossible, since it requires both interpolation and
extrapolation of the market data. Thus, it is more natural
to build the local volatility surface directly. In this talk
we present a generic semianalytical approach to calibrating
a parametric local volatility surface to the market data in
the realistic case when this data is sparse. This approach
also allows one to build a nonarbitrageable implied volatility
surface. The power of the method is illustrated by considering
layered local volatility and generating local and implied
volatility surfaces for options on SX5E.
This is a joint work with Artur Sepp.

Wed. October 26, 2011
5:00 p.m.

Matheus Grasselli , McMaster University
A dynamical systems model for credit expansion, asset price
bubbles and financial fragility
Hyman Minsky's main contribution to economics  the financial
instability hypothesis  links the expansion of credit to
fund new investment to the increase in asset prices and the
inherent fragility of an overleveraged financial system.
In this talk I describe an attempt to mathematize his model.
I start by reviewing the main properties of the Goodwin model
for employment and wages  a simple twodimensional ODE system
with globally stable cycles. I then describe the extension
of this model proposed by Steve Keen to incorporate financing
through a banking system. This threedimensional system exhibits
both a good equilibrium with a finite level of debt and a
bad one where debt grows without bounds. I analyze the stability
properties of this system, in particular with respect to interest
rates. A further extension connects this system to asset prices
and shows the destabilizing effect of Ponzi financing, that
is, the purchase of assets with borrowed money for purely
speculative purposes. In the final part of the talk I describe
the stabilizing effects of countercyclical government spending
and capital requirements.
=================
Bill Janeway, Senior Research Associate, Centre for Financial
Analysis and Policy, University of Cambridge and Senior Advisor,
Warburg Pincus
Tolerating Waste in the Innovation Economy or Putting
the 'Creative' in Creative Destruction
Over 250 years, economic development has been driven by waves
of transformational technology. This talk explores the three
phases of the Innovation Economy: (1) "upstream"
discovery and invention; (2) deployment of networked infrastructure;
and (3) "downstream" exploration of the new economic
space thereby created. Since the first and third phases are
necessarily implemented through repeated exercises in trial
and error, "Schumpeterian Waste" is inherent in
the process. Further, while deployment of new infrastructure
may be efficiently planned and executed, it has often been
characterized by redundant and unremunerative projects, whether
undertaken by the private or the public sectors. Thus, the
process of innovation is critically dependent upon sources
of funding relatively unconcerned with visible economic return.The
two principle sources of funding for the upstream phase of
discovery and invention have been the rents earned by monopoly
corporations and state programs of noneconomic investment,
often motivated by issues of national security. The downstream
phase of economic exploration has repeatedly been financed
through speculative bubbles in the financial markets. From
the canal and railway manias of the first and second industrial
revolutions through electrification and the internet in the
twentieth century, infrastructure investments have also been
funded by financial speculation. While transformational innovation
on the supply side of the economy transcends the normative
goal of efficient resource allocation, too great a concern
with efficient resource allocation can also encourage toleration
of macroeconomic waste: unemployed human and physical resources.
In turn, toleration of such "Keynesian Waste" can
feed back to inhibit development of the Innovation Economy.

Wed. Sept. 28, 2011
5:00 p.m.

Vadim Linetsky, McCormick School of Engineering and
Applied Sciences, Northwestern University
Unified CreditEquity Modeling: From SingleName to MultiName
This talk surveys our work on unified creditequity models
that view the stock price as the fundamental observable state
variable that jumps to zero in the event of the firm's default
on its debt and treat both credit derivatives and equity derivatives
in a unified fashion as contingent claims on the defaultable
stock price process. After surveying singlename models, we
present
multiname unified credit equity model.

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