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Abstracts for Workshop on Research in Financial Mathematics and Engineering




Peter Bloomfield and Xiaofeng He:
Credit Risk, Credit Quality Drift, and the Business Cycle

Credit risk is the possibility that a financial asset may lose value because of distress at another institution. A borrower may default on a loan, an issuer may suspend payments on a bond, a counterparty may be unable to meet its obligations under a derivative contract. The risk is measured by the size and term of the exposure and the probability of a loss. In the short term, the probability of loss is roughly proportional to the term, and the principal issue is variability in the exposure. In the long term, the exposure may be controlled in various ways, and the principal issue is the variability in the probability of loss. A series of downgrades may lead to a substantial increase in that probability. Our research focuses on the effect of market conditions on the frequency and direction of credit rating changes.



Donald Erdman:
Copulas and Large Scale Monte Carlo Simulation for Integrated Risk Measurement

Integrated firmwide risk measurement involves aggregating risk measures to the top of an organization across all markets, all financial instruments, and all counterparties while properly taking into account interrelationships between the sources of risk. In most cases, Monte Carlo simulation is the preferred method, since this makes possible the use of the most appropriate distributions for risk factors, including non-normal distributions. Multivariate non-normal models generally provide more accurate risk measures. But the challenge is to provide a framework for risk measurement with multivariate non-normal modeling that is tractable with a large number of risk factors. The solution is to estimate small dimensional models using appropriate distributions (GARCH, mean-reversion, mixture, etc.) and then integrate the resulting marginal distributions into a single consistent joint distribution using an appropriate copula. The details of this approach will be discussed in this presentation.



Paul Fackler:
Modeling Commodity Futures Term Structure

Recent work on multi-factor affine models of futures price term structure will be reviewed. Such model can incorporate important features of commodity price behavior, including stochastic volatility and seasonality, while retaining computational tractability. Uses of these models in risk management and projectvaluation will be discussed.


Jean-Pierre Fouque:
Black-Scholes, Implied Volatilities and Stochastic Volatility Models

We will review Black-Scholes pricing and hedging theory and discuss the observed "smile/skew" in S&P500 implied volatilities. Stochastic volatility models account for these effects but one has to deal with incompleteness. Corrections to Black-Scholes will be presented. Reference: Derivatives in financial markets with stochastic volatilty, by Fouque-Papanicolaou-Sircar.



William Smith:
Energy Business: Risks Involved with Electricity Trading

Electricity is one of the most recent commodities to be transformed by derivatives and risk management. Fundamental analysis tells us that energy markets respond to underlying price drivers that differ dramatically from interest rates and other well-developed money markets. More importantly, quantitative analysis tells us that the differences in these fundamental price drivers can exert a dramatic domino effect as they are applied to pricing and hedging models. This discussion will center on the nuances of electricity trading and in particular the risks faced by Duke Power's Bulk Power Marketing Group.



Christian Wypasek:
Competing Risks in the Modeling of Asset-backed Cash Flows

Risk analytics, particularly in the mortgage industry over the past decade, has evolved through credit scoring to the modeling of asset cashflows. After the oil patch collapse of the 80's and the the California recession of the early 90's, the initial goals were reducing propensity of default on new originations and the prediction of overall losses. Attention then turned towards risk-based pricing where the more predictive a scoring model, the more capable an underwriting system is at capturing the desirable portion of the market. Similarly, in the securitization arena, better analytics is a key to better execution for the issuer. The analytical needs for securitization include not only ultimate loss estimates, but also the multiple risks associated with the timing of defaults and prepayments. While Wall Street has historically used very simple hazard rate models on pools of loans to evaluate bond structures, the focus at the Structured Transactions and Analytical Research (STAR) group within First Union Securities has been on loan level models where possible. This presentation will discuss some of the modeling efforts within the STAR group to address competing risk issues, including marked point processes and Markov chains.



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