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, finace 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 45-minute 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.

### Upcoming Seminars

May 18, 2005 -- 5 p.m.

**Didier Sornette**, Professor of Geophysics at UCLA

*Extreme Financial Risks*

The frontal attack aiming at the determination of the multivariate
distribution of the asset returns is a challenging task and, in our
opinion, much less instructive and useful than the separate studies
of the marginal distributions of the asset returns on the one hand
and the intrinsic dependence structure of these assets on the other
hand. We offers an original and thorough treatment of these two domains,
focusing mainly on the concepts and tools that remain valid for large
and extreme price moves. Its originality lies in detailed and thorough
presentations of the state of the art on (i) the different distributions
of financial returns for various applications (VaR, stress testing)
and (ii) the most important and useful measures of dependences, both
unconditional and conditional and a study of the impact of conditioning
on the size of large moves on the measure of extreme dependences.
A large emphasis is thus put on the theory of copulas, their empirical
testing and calibration, as they offer intrinsic and complete measures
of dependences. Many of the results presented here are novel and have
not been published or have been recently obtained by the authors or
their colleagues and form the core of the book.

Y. Malevergne and D. Sornette

Extreme Financial Risks (from dependence to risk management) (Springer,
Heidelberg, 2005).

March 30, 2005 -- 5 p.m.

**Robert Almgren**, Director, Mathematical Finance Program, University
of Toronto

*Optimal Portfolios from Ordering Information*

Many years of finance literature have shown how to form portfolios
that minimize risk and maximise expected profit, using expected returns
for each asset in the portfolio. But often all that is available is
a ranking of the assets from best to worst; more generally the investor
may have a set of homogeneous inequality beliefs about the expected
returns that he or she wishes to combine with covariance information.
We present an elegant way to construct optimal portfolios based directly
on this sorting information, and show dramatic improvement over naive
strategies using both simulated and real data. (Joint work with Neil
Chriss; paper available at SSRN http://papers.ssrn.com/sol3/papers.cfm?abstract_id=633801
)..

February 23, 2005 -- 5 p.m.

**Tom Hurd**, McMaster University and director of PhiMac

*Fast CDO pricing in an affine Markov chain model of credit risk*

It is shown that credit basket derivatives, such as CDSs which depend
on a large number of firms, can be priced in a parsimonious and computationally
efficient manner within a new model for multifirm credit migration.
This affine Markov chain (AMC) model gives each firm a credit rating
that migrates according to a Markov chain. The dependence between
the chains derives from a stochastic time change, which is combined
with stochastic interest and recovery rates. The model can be flexibly
fit to observed market bond data for the constituent firms. It gives
good reproduction of essential features such as credit spread curves,
default correlations and multifirm default distributions. This is
joint work with A. Kuznetsov.

November 24, 2004 -- 5:00 p.m.

**Vicky Henderson, **Princeton** **University

*Valuing the Option to Invest in an Incomplete Market*

This paper analyzes a new model for irreversible investment under
uncertainty. The main question we address is how incompleteness and
managerial risk-aversion to idiosyncratic risks impacts on the value
of the option to invest and the investment timing decision. In contrast,
existing

classic models rely on capital market completeness (via a perfect
spanning asset) or, as in McDonald and Siegel (1986), risk-neutrality
towards idiosyncratic risks. Both types of model are limiting cases
of our incomplete one.

Our main conclusions are that risk-aversion to idiosyncratic risks
induces the manager to place less value on the option and invest earlier
than the classic models suggest. In fact, there is a qualitative difference
in the investment recommendations of the models, and we show that
approximating

an incomplete situation with a risk-neutral or McDonald and Siegel
(1986) solution can result in an incorrect investment decision. As
such, our incomplete framework gives a much richer model of investment
under uncertainty.

**David Hobson, **Mathematical Sciences , University of Bath

*Local martingales and Option prices*

In this talk we are interested in option pricing in markets with
bubbles. A bubble is defined to be a price process which, when discounted,
is a local martingale under the risk-neutral measure but not a martingale.

We give examples of bubbles both where volatility increases with the
price level, and where the bubble is the result of a feedback mechanism.

In a market with a bubble many standard results from the folklore
become false. Put-call parity fails, the price of an American call
exceeds that of a European call and prices are no longer convex in
the underlying. We show how these results must be modified in the
presence of a bubble. It turns out that the option value depends critically
on the definition of admissible strategy, and that the standard mathematical
definition may not be consistent with the definitions used for trading.

October 27, 2004 -- 5:00 p.m.

**Stanley R Pliska,** Finance Department, University of Illinois
at Chicago

*Optimal Mortgage Refinancing with Endogenous Mortgage Rates: an
Intensity Based, Equilibrium Approach*

Using recent, intensity based, continuous time results by Goncharov
on endogenous mortgage rates, we develop analogous results via a discrete
time model where interest rates (and possibly other exogenous factors)
comprise a Markov chain. As with Goncharov, arbitrage considerations
and the specifications of the mortgagor's prepayment behavior lead
to a unique process for mortgage rates. We then formulate a mortgagor's
optimal refinancing problem as a Markov decision chain, where the
mortgage rates are exogenous and the mortgagor acts so as to minimize
the present of the cash flow (including refinancing costs). We then
proceed to consider the equilibrium problem where the mortgagor is
a representative agent who acts optimally and, given this behavior,
the mortgage rates are consistent with no arbitrage. Existence of
an equilibrium solution is established via Markov decision theory,
and a numerical example is presented.

**Thaleia Zariphopoulou**, University of Texas at Austin

*Derivative valuation and investment management *

**Change** T. Zariphopoulou's talk will not take place on October
27, 2004.

It will be rescheduled for Spring 2005

September 29, 2004 --5:00 p.m.

**Luis A. Seco**, Risklab and Department of Mathematics, University
of Toronto

Pricing Default Correlation Products within a structural framework

Evaluating the joint probability of default is an important task
in credit derivative pricing and credit risk management. The market
for exotic derivatives with payoffs contingent on the credit quality
of a number of reference entities has grown considerably over recent
years. Non-linear credit portfolios are quite common all over the
world. However the valuation of such structures is technically difficult;
most credit models fail to reliably capture multiple defaults. In
this paper we discuss the joint distribution of first-passage-time
structural models, within a Gaussian framework, providing analytical
formulas and approximations for the case of more than two underlying
credits components. We will apply this to the pricing of CDS's and
CDO's. This is joint work with Marcos Escobar.

**Mark Kamstra**, Schulich School of Business, York University

*Investing Confidence in the Ex Ante Equity Premium:*

A New Methodology and A Narrower Range of Estimates

**Abstract**: The equity premium is the extra return investors
anticipate when purchasing risky stock instead of risk-free debt.
Over the past century, US stocks have returned roughly 6% more than
risk-free debt, which is much higher than warranted by standard economic
theory. Several studies suggest the equity premium has fallen in recent
years. However, since all equity premium estimates reported to date
are very imprecise, even the new, lower estimates are insignificantly
different from puzzlingly high values of the equity premium. Many
estimates of the ex ante equity premium in the literature have confidence
intervals of 600 to 1000 basis points. Some of the more recent estimates
are as narrow as 320 to 800 basis points. Based on our new technique,
we are able to further narrow the range to 100 to 150 basis points.
We believe with great confidence that the true ex ante equity premium
lies within 50 or 75 basis points of 3.5%. The degree of precision
depends on whether we believe the ex ante equity premium is constant,
downward trending, autocorrelated, etc.

Our contribution is based on a new method that simulates the distribution
from which ex post equity premia are drawn. By comparing statistics
that arise from our simulations with key financial characteristics
of the US economy, including dividend yields, Sharpe ratios, and interest
rates, we are able to substantially narrow the confidence bound on
equity premium estimates. We consider a range of data generating processes
incorporating empirically validated features such as a downward trending
equity premium, a structural break in the equity premium time series
process, sampling uncertainty in generating model parameters, investor
uncertainty in estimating model parameters, and cross-correlation
between interest rates, dividend growth rates, and equity premia.
The result of our analysis is by far the most precise estimate that
has been reported in the literature to date.

back to top