WSC 2003 Final Abstracts

Applications of Simulation Models in Finance and Insurance
Thomas N. Herzog (U.S. Department of Housing & Urban Development) and Graham Lord (Princeton University)

Abstract:
We describe a number of applications of simulation methods to practical problems in finance and insurance. The first entails the simulation of a two-stage model of a property-casualty insurance operation. The second application simulates the operation of an insurance regime for home equity conversion mortgages (also known as reverse mortgages). The third is an application of simulation in the context of Value at Risk, a widely-used measure for assessing the performance of portfolios of assets and/or liabilities. We conclude with an application of simulation in the testing of the efficient market hypothesis of the U.S. stock market.

Efficient Simulations for Option Pricing
Jeremy Staum (Northwestern University)

Abstract:
This paper presents an overview of techniques for improving the efficiency of option pricing simulations, including quasi-Monte Carlo methods, variance reduction, and methods for dealing with discretization error.

Importance Sampling for a Mixed Poisson Model of Portfolio Credit Risk
Paul Glasserman and Jingyi Li (Columbia University)

Abstract:
Simulation is widely used to estimate losses due to default and other credit events in financial portfolios. The challenge in doing this efficiently results from (i) rare-event aspects of large losses and (ii) complex dependence between defaults of multiple obligors. We discuss importance sampling techniques to address this problem in two portfolio credit risk models developed in the financial industry, with particular emphasis on a mixed Poisson model. We give conditions for asymptotic optimality of the estimators as the portfolio size grows.

Rare-Event, Heavy-Tailed Simulations Using Hazard Function Transformations, with Applications to Value-at-Risk
Zhi Huang and Perwez Shahabuddin (Columbia University)

Abstract:
We develop an observation that a simulation method introduced recently for heavy-tailed stochastic simulation, namely hazard-rate twisting, is equivalent to doing exponential twisting on a transformed version of the heavy-tailed random-variable; the transforming function is the hazard function. Using this approach, the paper develops efficient methods for computing portfolio value-at-risk (VAR) when changes in the underlying risk factors have the multivariate Laplace distribution.

Genetic Programming with Monte Carlo Simulation for Option Pricing
N. K. Chidambaran (Rutgers University)

Abstract:
I examine the role of programming parameters in determining the accuracy of Genetic Programming for option pricing. I use Monte Carlo simulations to generate stock and option price data needed to develop a Genetic Option Pricing Program. I simulate data for two different stock price processes – a Geometric Brownian process and a Jump-Diffusion process. In the jump-diffusion setting, I seed the Genetic Program with the Black-Scholes equation as a starting approximation. I find that population size, fitness criteria, and the ability to seed the program with known analytical equations, are important determinants of the efficiency of Genetic Programming.

Crystal Ball for Six Sigma Tutorial
Lawrence I. Goldman and Ethan Evans-Hilton (Decisioneering, Inc.) and Hilary Emmett (Decisioneering (UK) Ltd.)

Abstract:
In an increasingly competitive market, businesses are turning to new practices like Six Sigma, a structured methodology for accelerated process improvement, to help reduce costs and increase efficiency. Monte Carlo simulation can help Six Sigma practitioners understand the variation inherent in a process or product, and in turn, can be used to identify and test potential improvements. The benefits of understanding and controlling the sources of variability include increased productivity, reduced waste, and sales driven through improved customer satisfaction. This tutorial uses Crystal Ball® Professional Edition, a suite of easy-to-use Microsoft Excel add-in software, to demonstrate how stochastic simulation and optimization can be used in a Six Sigma analysis of a technical support call center.

OptFolio … A Simulation Optimization System for Project Portfolio Planning
Jay April, Fred Glover, and James P. Kelly (OptTek Systems, Inc.)

Abstract:
OptFolio is a new portfolio optimization software system simultaneously addresses financial return goals, catastrophic loss avoidance, and performance probability. The innovations embedded in the system enable users to confidently design effective plans for achieving financial goals, employing accurate analysis based on real data. State-of-the-art technology integrates simulation and metaheuristic optimization techniques and a new surface methodology based on linear programming into a global system that guides a series of evaluations to reveal truly optimal investment scenarios. Portfolio analysis tools are designed to aid senior management in the development and analysis of portfolio strategies, by giving them the capability to assess the impact on the corporation of various investment decisions. In this paper we will present new techniques that increase the flexibility of optimization tools and deepen the types of portfolio analysis that can be carried out. We include examples applied to energy, pharmaceutical, and information technology portfolios.

Work Reduction in Financial Simulations
Jeremy Staum (Northwestern University) and Samuel Ehrlichman and Vadim Lesnevski (Cornell University)

Abstract:
We investigate the possibility of efficiency gains from schemes that reduce the expected cost of a simulated path, which allows more paths given a fixed computational budget. Many such schemes impart bias, so we look at the bias-variance tradeoff in terms of mean squared error. The work reduction schemes we consider are fast numerical evaluation of functions, such as the exponential, as well as changes to simulation structure and sampling schemes. The latter include descriptive sampling, reducing the number of time steps, and dispensing with some factors in a multi-factor simulation. In simulations where computational budgets are tightly constrained, such as risk management and calibration of financial models, using cheaper, less accurate algorithms can reduce mean squared error.

Efficient Simulation of Gamma and Variance-Gamma Processes
Athanassios N. Avramidis, Pierre L'Ecuyer, and Pierre-Alexandre Tremblay (University of Montreal)

Abstract:
We study algorithms for sampling discrete-time paths of a gamma process and a variance-gamma process, defined as a Brownian process with random time change obeying a gamma process. The attractive feature of the algorithms is that increments of the processes over longer time scales are assigned to the first sampling coordinates. The algorithms are based on having in explicit form the process' conditional distributions, are similar in spirit to the Brownian bridge sampling algorithms proposed for financial Monte Carlo, and synergize with quasi-Monte Carlo techniques for efficiency improvement. We compare the variance and efficiency of ordinary Monte Carlo and quasi-Monte Carlo for an example of financial option pricing with the variance-gamma model.

Duality Theory and Simulation in Financial Engineering
Martin B. Haugh (Columbia University)

Abstract:
This paper presents a brief introduction to the use of duality theory and simulation in financial engineering. It focuses on American option pricing and portfolio optimization problems when the underlying state space is high-dimensional. In general, it is not possible to solve these problems exactly due to the so-called ``curse of dimensionality'' and as a result, approximate solution techniques are required. Approximate dynamic programming (ADP) and dual based methods have recently been proposed for constructing and evaluating good approximate solutions to these problems. In this paper we describe these ADP and dual-based methods, and the role simulation plays in each of them. Some directions for future research are also outlined.

Simulation Methods for Risk Analysis of Collateralized Debt Obligations
William J. Morokoff (Moody's KMV)

Abstract:
Collateralized Debt Obligations (CDOs) are sophisticated financial products that offer a range of investments, known as tranches, at varying risk levels backed by a collateral pool typically consisting of corporate debt (bonds, loans, default swaps, etc.). The analysis of the risk-return properties of CDO tranches is complicated by the highly non-linear and time dependent relationship between the cash flows to the tranche and the underlying collateral performance. This paper describes a multiple time step simulation approach that tracks cash flows over the life of a CDO deal to determine the risk characteristics of CDO tranches.

Simulation and Optimization for Real Options Valuation
Barry R. Cobb and John M. Charnes (The University of Kansas)

Abstract:
Real options valuation (ROV) considers the managerial flexibility to make ongoing decisions regarding implementation of investment projects and deployment of real assets. This paper introduces a simulation-optimization approach to valuing real investment options based on a model containing several decision variables and realistic stochastic inputs. Using this approach, the value of a portfolio of real investment projects is determined by maximizing the mean discounted cash flows calculated by the model over many combinations of the decision variables. This yields an optimal decision rule that significantly increases the value extracted from the investment projects in comparison to arbitrary decision rules.

A New Methodology to Evaluate the Real Options of an Investment Using Binomial Trees and Monte Carlo Simulation
Michele Amico (University of Palermo), Zbigniew J. Pasek and Farshid Asl (University of Michigan) and Giovanni Perrone (University of Basilicata)

Abstract:
This paper deals with a new methodology to evaluate the real operating options embedded in a manufacturing system investment. In a single product framework, the demand is assumed as the main source of uncertainty, therefore as a stochastic variable following a Geometric Brownian Motion (GBM). Then, focusing on the real option to expand the capacity at a certain time in the future, we have developed a new approach for the option payoff, looking forward in the time interval from the expansion date to the end of the planning horizon. The payoff function is the expected Net Present Value (NPV), at the expansion date, of the additional investment to increase the capacity, and it is calculated using Monte Carlo simulation. The option value is computed with a binomial tree algorithm. A numerical example and a sensitivity analysis of the option value as a function of some parameters are finally presented.

A Simulation-Based Credit Default Swap Pricing Approach Under Jump-Diffusion
Tarja Joro (University of Alberta) and Paul Na (Bayerische Landesbank New York Branch)

Abstract:
Diffusion-based Credit Default Swap (CDS) pricing models produce zero spreads for very short-term contracts, which contradict empirical data. We introduce a simulation-based CDS pricing approach that avoids the zero short-term spreads problem through a jump-diffusion process.

Risk Management of a P/C Insurance Company Scenario Generation, Simulation and Optimization
John M. Mulvey and Hafize Gaye Erkan (Princeton University)

Abstract:
A large conglomerate such as a property/casualty insurance firm in this case, can be divided along business boundaries. This division might be along commercial lines, homeowner lines and perhaps across countries. An insurance firm’s capital can be interpreted as a buffer that protects the company from insolvency and its inability to pay policyholder losses. Rare events have been simulated over the two divisions of an insurance firm. Different risk measures like conditional value at risk (CVaR) have been implemented into the optimization model. Decomposition methods will be applied in the context of decentralized decision making of a multi-divisional firm.

A Two-Component Spot Pricing Framework for Loss-Rate Guaranteed Internet Service Contracts
Aparna Gupta, Lingyi Zhang, and Shivkumar Kalyanaraman (Rensselaer Polytechnic Institute)

Abstract:
The technological advances in recent years are allowing Internet Service Providers (ISPs) to provide Quality of Service (QoS) assurance for traffic through their domains. This article develops a spot pricing framework for intra-domain expected bandwidth contract with a loss based QoS guarantee. The framework accounts for both the cost and the risks associated with QoS delivery. A nonlinear pricing scheme is used in pricing for cost recovery; a utility based options pricing approach is developed for risk related pricing. The application of options pricing in Internet services provides a mechanism for fair risk sharing between the provider and the customer, and may be extended to price other uncertainties in QoS guarantees.