Seminar: Spring 2004

Viktor Spivakovsky (Citadel Investment Group)

Efficient computation of the loss probability distribution of a risky portfolio has become increasingly important in the past several years, motivated by the growing popularity of basket credit derivatives. The talk will present an overview of semianalytic methods for deriving the loss distribution when portfolio defaults are independent. These methods can be used in the conditional independence setting to derive the loss distribution for dependent portfolio defaults. Some practical applications of these models will be discussed.
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Tiong Wee Lim (Stanford University, and National University of Singapore)

In the presence of transaction costs, it is no longer possible to perfectly replicate the payoff of a European option by trading in the underlying stock. We present a new option hedging strategy based on minimizing the expected cumulative hedging error and additional cost of rebalancing due to proportional transaction costs. The resulting singular stochastic control problem can be related to an optimal stopping problem, which we solve to show that an optimal hedge consists of selling/buying the underlying stock whenever the number of shares held falls above/below a no-transaction band about the "delta". We also discuss a new approach to pricing using market data on the stock and options, and consider the optimal hedge in the presence of transaction costs. This is joint work with T.L. Lai.
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Chuck Lucas (AIG)

Life insurance and annuity products sold globally increasingly contain features, such as guaranteed minimum death benefits, which cannot be modeled properly with traditional actuarial approaches, leading to increasing use of stochastic methodologies commonly used in valuation and risk management of financial options.

This presentation will discuss approaches to this problem taken by AIG, stressing implications for institutional change, organization and risk management, product and market development, internal culture change and infrastructure impacts. Implications will be drawn with respect to potential directions for research in financial mathematics.
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Terry Benzschawel (Citigroup Global Markets)

I describe results of empirical studies of historical spreads in the corporate bond market and show how spread changes, regardless of credit rating, are largely determined by a single common variable. In addition, I calculate the component of corporate credit spreads due to default probability and report analyses of the residual spreads as functions of credit quality and duration.

Analysis of spread changes for other spread markets (e.g. asset-backeds, emerging markets, etc.) reveal a large, but smaller, degree of spread co-movement across sectors and indicate that sector spreads trend and mean revert on roughly similar time scales. That is, spread changes trend in the short term (under two years) and mean-revert over longer periods.

That information, along with the CAPM and our strategists' monthly outlooks, was used to construct a cross-sector asset allocation model that consistently outperformed a benchmark portfolio in ten years of out-of-sample testing.
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Vineer Bhansali (PIMCO)

Interest rate swap spreads play a crucial role in the valuation of fixed income securities. I will first review what we have learnt about the dynamics of swap spreads over the last decade with the evolution of derivatives markets and new empirical data.

Then I will disuss the evolution of new generations of models for valuation of spread products. The talk will link this important area to the general issue of consistent risk measurement and relative value in today's global bond markets.
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Darrell Duffie (Stanford University)

I will compare current leading stochastic models of default by corporations. Competing approaches to the joint distribution of multi-firm default times include: (1) parametric copula models, and (2) doubly-stochastic (Cox) counting processes. The burgeoning market for credit derivatives and new capital regulations for banks have triggered a high-stakes search for an acceptable "standard approach." I will present empirical regularities connecting firm-specific default covariates (leverage and volatility), macro-economic performance, the market pricing of credit risk (default-swap rates), and the clustering of U.S. corporate default times since 1972.
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Justin Wolfers (Stanford University)

We analyze the extent to which simple markets can be used to aggregate disperse information into efficient forecasts of uncertain future events. Drawing together data from a range of prediction contexts, we show that market-generated forecasts are typically fairly accurate, and that they outperform most moderately sophisticated benchmarks. Carefully designed contracts can yield insight into the market's expectations about probabilities, means and medians, and also uncertainty about these parameters. Moreover, conditional markets can effectively reveal the market's beliefs about regression coefficients, although we still have the usual problem of disentangling correlation from causation. We discuss a number of market design issues and highlight domains in which prediction markets are most likely to be useful.
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Amnon Levy (Moody's KMV)

I will discuss the problem of analyzing a portfolio of credit risky instruments. The discussion will revolve around current approaches, along with their associated challenges. The talk will explore the details of the models upon which Portfolio Manager is built - a quantitative tool developed by Moody's KMV that analyzes credit portfolio risk.

The talk will address questions such as: How much economic capital does a portfolio require to support our desired debt rating? Given the amount of capital, are we earning an appropriate return on capital? Which are our most attractive exposures from a risk/return perspective? Which are our least attractive?
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Galin Georgiev (PAAMCO)

The talk will address unrelated open problems in two different fields:
1) Active portfolio management: A problem faced by most multi-strategy hedge funds and fund-of-funds is evaluating the performance of the different sub-strategies (and sub-managers) in real time especially when the latter are relatively new and have no back-tested or other track record. The absolute performance (risk-adjusted or not) in any one time period is not a good measure because it does not take into account and does not adjust for the performance of the overall book during this period.

2) Microstructure: The problem is how to define and study analytically the so-called "market impact" of trading which is the impact on the price of a trade of given size. There are number of different definitions and approaches both in one- and multi-dimensional context (using impulse-response function etc.) We discuss the shape of the "market impact" function and whether or not it is properly defined.
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