June 18, 2024

The Fields Institute 2004-2005
Seminar Series on Quantitative Finance

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, 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 )..

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.

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