COMMERCIAL AND INDUSTRIAL MATHEMATICS

2008-2009
Seminar Series on Quantitative Finance
held at the Fields Institute, 222 College St., Toronto

sponsored by

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. Information-based 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.]

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 year-database 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 over-the-counter 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).

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 look-back 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 Black-Cox 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 time-changed 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.

"CANCELLED"

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: Under-diversification and Asset Selection
We offer a rational explanation for the observed under-diversification 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, simulation-based, 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 cross-sectional implications of financial constraints in an overlapping-generations model and discuss the potential of financial constraints in explaining observed deviations from the predictions of the Capital Asset Pricing Model.

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 ill-suited 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 well-accepted option pricing models. The most puzzling finding in the existing literature, the large returns to writing out-of-the-money puts, are not inconsistent (i.e., are statistically insignificant) relative to the Black-Scholes 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 market-neutral portfolios such as straddles or delta-hedged returns. The returns on these portfolios can be explained by jump risk premia and estimation risk.

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 multi-period data to long horizon loss distributions (typically one year for economic capital calculations and longer term for ratings analyses) will also be discussed.