A two-stage stochastic integer programming approach

We present an algorithmic approach for solving two-stage stochastic mixed 0-1 problems. The first stage constraints of the Deterministic Equivalent Model have 0--1 variables and continuous variables. The approach uses the Twin Node Family (TNF) concept within the algorithmic framework so-called {Branch-and-Fix Coordination} for satisfying the {nonanticipativity} constraints, jointly with a Benders Decomposition scheme for solving a given {LP} model at each {TNF} integer set. As an illustrative case, the structuring of a portfolio of Mortgage-Backed Securities under uncertainty in the interest rate path along a given time horizon is used. Some computational experience is reported.This research has been partially support by the grant Grupo consolidado de alto rendimiento 9/UPV 00038.321-13631/2001 from UPV, the project MEC2001-0636 from the DGCIT, the Researchers’ Education grant program 2000 from Gobierno Vasco, and the grant GRUPOS79/04 from the Generalitat Valenciana, Spain

Extending the MAD Portfolio Optimization Model to Incorporate Downside Risk Aversion

The mathematical model of portfolio optimization is usually expected as a bicriteria optimization problem where a reasonable trade-off between expected rate of return risk is sought. In a classical Markowitz model the risk is measured by a variance, thus resulting in a quadratic programming model. As an alternative, the MAD model was proposed where risk is measured by (mean) absolute deviation instead of a variance. The MAD model is computationally attractive, since it is transformed into an easy to solve linear programming program. In this paper we present an extension to the MAD model allowing to account for downside risk aversion of an investor, and at the same time preserving simplicity and linearity of the original MAD model

Monetary Policy, Regulation and Volatile Markets

Turmoil in financial markets causes reflection. Is monetary policy conducted in the most efficient way? Are regulatory and supervisory arrangements adequate when market volatility increases and financial institutions come under stress? In the present SUERF Study, we have collected the reflections by an outstanding group of top officials, researchers and observers. The editors are proud to be able to present their joint insights to SUERF readers. The papers were presented at the 27th SUERF Colloquium in Munich in June 2008: New trends in asset management: Exploring the implications.Financial markets, volatility, regulatory and supervisory arrangements, LATW, bubbles, monetary policy, asset prices, interest rate policy, LTCM, Basel II, MiFID, subprime, CDOs

WARNING: Physics Envy May Be Hazardous To Your Wealth!

The quantitative aspirations of economists and financial analysts have for many years been based on the belief that it should be possible to build models of economic systems - and financial markets in particular - that are as predictive as those in physics. While this perspective has led to a number of important breakthroughs in economics, "physics envy" has also created a false sense of mathematical precision in some cases. We speculate on the origins of physics envy, and then describe an alternate perspective of economic behavior based on a new taxonomy of uncertainty. We illustrate the relevance of this taxonomy with two concrete examples: the classical harmonic oscillator with some new twists that make physics look more like economics, and a quantitative equity market-neutral strategy. We conclude by offering a new interpretation of tail events, proposing an "uncertainty checklist" with which our taxonomy can be implemented, and considering the role that quants played in the current financial crisis.Comment: v3 adds 2 reference

Tranching and Pricing in CDO-Transactions

This paper empirically investigates the tranching and tranche pricing of European securitization transactions of corporate loans and bonds. Tranching allows the originator to issue bonds with strong quality differences and thereby attract heterogeneous investors. We find that the number of differently rated tranches in a transaction is inversely related to the quality of the underlying asset pool. Credit spreads on tranches in a transaction are inversely related to the number of tranches. The average price for transferring a unit of expected default risk, paid in a transaction, is inversely related to the default probability of the underlying asset pool. The average price, paid for a tranche, increases with the rating of the tranche, it is higher for the lowest rated tranche and very high for AAA-tranches in true sale-transactions. It varies little across butterfly spreads obtained from rated tranches except for the most senior spread.Securitization, information asymmetries, tranching of asset portfolios, risk premiums of tranches

Information asymmetries and securitization design

The strong growth in collateralized debt obligation transactions raises the question how these transactions are designed. The originator designs the transaction so as to maximize her benefit subject to requirements imposed by investors and rating agencies. An important issue in these transactions is the information asymmetry between the originator and the investors. First Loss Positions are the most important instrument to mitigate conflicts due to information asymmetry. We analyse the optimal size of the First Loss Position in a model and the actual size in a set of European collateralized debt obligation transactions. We find that the asset pool quality, measured by the weighted average default probability and the diversity score of the pool, plays a predominant role for the transaction design. Characteristics of the originator play a small role. A lower asset pool quality induces the originator to take a higher First Loss Position and, in a synthetic transaction, a smaller Third Loss Position. The First Loss Position bears on average 86 % of the expected default losses, independent of the asset pool quality. This loss share and the asset pool quality strongly affect the rating and the credit spread of the lowest rated tranche.Securitization, collateralized debt obligations, asset pool quality, First Loss Position, synthetic transactions, tranching

QUANTIFYING THE VALUE OF MODELS AND DATA: A COMPARISON OF THE PERFORMANCE OF REGRESSION AND NEURAL NETS WHEN DATA QUALITY VARIES

Under circumstances where data quality may vary, knowledge about the potential performance of alternate predictive models can enable a decision maker to design an information system whose value is optimized in two ways. The decision maker can select a model which is least sensitive to predictive degradation in the range of observed data quality variation. And, once the "right" model has been selected, the decision maker can select the appropriate level of data quality in view of the costs of acquiring it. This paper examines a real-world example from the field of finance -- prepayments in mortgage-backed securities (MBS) portfolio management -- to illustrate a methodology that enables such evaluations to be made for two modeling alternative: regression analysis and neural network analysis. The methodology indicates that with "perfect data," the neural network approach outperforms regression in terms of predictive accuracy and utility in a prepayment risk management forecasting system (RMFS). Further, the performance of the neural network model is more robust under conditions of data quality degradation.Information Systems Working Papers Serie

A Two-Period Portfolio Selection Model for Asset-backed Securitization

Asset-Backed Securitization (ABS) is a well-stated financial mechanism which allows an institution (either a commercial bank or a firm) to get funds through the conversion of assets into capital market products called notes or asset-backed securities. In this paper, we analyze the combinatorial problem faced by the financial institution which has to optimally select the set of assets to be converted into notes. We assume that assets follow an amortization rule characterized by constant periodic principal installments (Italian amortization). The particular shape of the assets outstanding principal is exploited both in the mathematical formulation of the problem and in its solution. In particular, we study a model formulation for the special case where assets selection occurs at two dates during the securitization process. We introduce two heuristic approaches based on Lagrangian relaxation and analyze their worst-case behavior compared to the optimal solution value. The performance of the algorithms is tested on a large set of problem instances generated according to two real-world scenarios provided by a leasing company. The proposed approximation algorithms turn out to yield solutions of high quality within very short computation time. The comparison to the solution approach applied by practitioners yields an average improvement of roughly 10% of the objective function value