Quasi-Monte Carlo Methods in Cash Flow Testing Simulations

What actuaries call cash flow testing is a large-scale simulation pitting a company\u27\u27s current policy obligation against future earnings based on interest rates. While life contingency issues associated with contract payoff are a mainstay of the actuarial sciences, modeling the random fluctuations of US Treasury rates is less studied. Furthermore, applying standard simulation techniques, such as the Monte Carlo method, to actual multi-billion dollar companies produce a simulation that can be computationally prohibitive. In practice, only hundreds of sample paths can be considered, not the usual hundreds of thousands one might expect for a simulation of this complexity. Hence, insurance companies have a desire to accelerate the convergence of the estimation procedure. The paper reports the results of cash flow testing simulations performed for Conseco L.L.C. using so-called quasi-Monte Carlo techniques. In these, pseudo-random number generation is replaced with deterministic low discrepancy sequences. It was found that by judicious choice of subsequences, that the quasi-Monte Carlo method provided a consistently tighter estimate than the traditional methods for a fixed, small number of sample paths. The techniques used to select these subsequences are discussed

Modeling and quasi-Monte Carlo simulation of risk in credit portfolios

Credit risk is the risk of losing contractually obligated cash flows promised by a counterparty such as a corporation, financial institution, or government due to default on its debt obligations. The need for accurate pricing and hedging of complex credit derivatives and for active management of large credit portfolios calls for an accurate assessment of the risk inherent in the underlying credit portfolios. An important challenge for modeling a credit portfolio is to capture the correlations within the credit portfolio. For very large and homogeneous portfolios, analytic and semi-analytic approaches can be used to derive limiting distributions. However, for portfolios of inhomogeneous default probabilities, default correlations, recovery values, or position sizes, Monte Carlo methods are necessary to capture their underlying dynamic evolutions. Since the feasibility of the Monte Carlo methods is limited by their relatively slow convergence rate, methods to improve the efficiency of simulations for credit portfolios are highly desired. In this dissertation, a comparison of the commonly employed single step models for credit portfolios, referred to as the copula-based default time approach, with our novel applications of multi-step models was made at first. Comparison of simulation results indicates that the dependency structure may be better incorporated by the multi-step models, since the default time models can introduce substantially skewed correlations within credit portfolios, a shortcoming which has become more evident in the recent subprime crisis. Next, to improve the efficiency of simulations, quasi- random sequences were introduced into both the single step and multi-step models by devising several new algorithms involving the Brownian bridge construction and principal component analysis. The simulation results from tests under various scenarios suggest that quasi-Monte Carlo methods can substantially improve simulation effectiveness not only for the problems of computing integrals but also for those of order statistics, indicating significant advantage when calculating a number of risk quantities such as Value at Risk (VaR). Finally, the performance of the simulations based on the above credit portfolio models and the quasi-Monte Carlo methods was examined in the context of modeling and valuation of credit portfolio derivatives. The results suggest that these methods can considerably improve the simulation of complex financial instruments involving portfolio credit risk

Instrumental variables quantile regression for panel data with measurement errors

This paper develops an instrumental variables estimator for quantile regression in panel data with fixed effects. Asymptotic properties of the instrumental variables estimator are studied for large N and T when Na/T ! 0, for some a > 0. Wald and Kolmogorov-Smirnov type tests for general linear restrictions are developed. The estimator is applied to the problem of measurement errors in variables, which induces endogeneity and as a result bias in the model. We derive an approximation to the bias in the quantile regression fixed effects estimator in the presence of measurement error and show its connection to similar effects in standard least squares models. Monte Carlo simulations are conducted to evaluate the finite sample properties of the estimator in terms of bias and root mean squared error. Finally, the methods are applied to a model of firm investment. The results show interesting heterogeneity in the Tobin’s q and cash flow sensitivities of investment. In both cases, the sensitivities are monotonically increasing along the quantiles

A machine learning approach to portfolio pricing and risk management for high-dimensional problems

We present a general framework for portfolio risk management in discrete time, based on a replicating martingale. This martingale is learned from a finite sample in a supervised setting. The model learns the features necessary for an effective low-dimensional representation, overcoming the curse of dimensionality common to function approximation in high-dimensional spaces. We show results based on polynomial and neural network bases. Both offer superior results to naive Monte Carlo methods and other existing methods like least-squares Monte Carlo and replicating portfolios.Comment: 30 pages (main), 10 pages (appendix), 3 figures, 22 table

Real Option Valuation of a Portfolio of Oil Projects

Various methodologies exist for valuing companies and their projects. We address the problem of valuing a portfolio of projects within companies that have infrequent, large and volatile cash flows. Examples of this type of company exist in oil exploration and development and we will use this example to illustrate our analysis throughout the thesis. The theoretical interest in this problem lies in modeling the sources of risk in the projects and their different interactions within each project. Initially we look at the advantages of real options analysis and compare this approach with more traditional valuation methods, highlighting strengths and weaknesses ofeach approach in the light ofthe thesis problem. We give the background to the stages in an oil exploration and development project and identify the main common sources of risk, for example commodity prices. We discuss the appropriate representation for oil prices; in short, do oil prices behave more like equities or more like interest rates? The appropriate representation is used to model oil price as a source ofrisk. A real option valuation model based on market uncertainty (in the form of oil price risk) and geological uncertainty (reserve volume uncertainty) is presented and tested for two different oil projects. Finally, a methodology to measure the inter-relationship between oil price and other sources of risk such as interest rates is proposed using copula methods.Imperial Users onl

The History of the Quantitative Methods in Finance Conference Series. 1992-2007

This report charts the history of the Quantitative Methods in Finance (QMF) conference from its beginning in 1993 to the 15th conference in 2007. It lists alphabetically the 1037 speakers who presented at all 15 conferences and the titles of their papers.