WSC 2002 Final Abstracts

Simulation in Financial Engineering
Jeremy Staum (Cornell University)

Abstract:
This paper presents an overview of the use of simulation algorithms in the field of financial engineering, assuming on the part of the reader no familiarity with finance and a modest familiarity with simulation methodology, but not its specialist research literature. The focus is on the challenges specific to financial simulations and the approaches that researchers have developed to handle them, although the paper does not constitute a comprehensive survey of the research literature. It offers to simulation researchers, professionals, and students an introduction to an application of increasing significance both within the simulation research community and among financial engineering practitioners.

Importance Sampling for Multimodal Functions and Application to Pricing Exotic Options
Athanassios N. Avramidis (University of Montreal)

Abstract:
We consider importance sampling (IS) to increase the efficiency of Monte Carlo integration, especially for pricing exotic options where the random input is multivariate Normal. When the importance function (the product of integrand and original density) is multimodal, determining a good IS density is a difficult task. We propose an Automated Importance Sampling Density Estimation Procedure (AISDE). AISDE selects an IS density as a mixture of multivariate Normal densities with modes at certain local maxima of the importance function. When the simulation input is multivariate Normal, we use principal component analysis to obtain a reduced-dimension, approximate importance function, which allows efficient identification of a good IS density via AISDE in original problem dimensions over 100. We present Monte Carlo experimental results on randomly generated option-pricing problems (including path-dependent options), demonstrating large and consistent efficiency improvement.

Enhanced Quasi-Monte Carlo Methods with Dimension Reduction
Junichi Imai (Iwate Prefectural University) and Ken Seng Tan (University of Waterloo)

Abstract:
In recent years, the quasi-Monte Carlo approach for pricing high-dimensional derivative securities has been used widely relative to other competitive approaches such as the Monte Carlo methods. Such success can be, in part, attributed to the notion of effective dimension of the finance problems. In this paper, we provide additional insight on the connection between the effective dimension and the quasi-Monte Carlo method. We also propose a dimension reduction technique which further enhances the quasi-Monte Carlo method for derivative pricing. The efficiency of the proposed method is illustrated by applying it to high-dimensional multi-factor path-dependent derivative securities.

Credit Risk Modeling for Catastrophic Events
Tarja Joro (University of Alberta School of Business) and Paul Na (Bayerische Landesbank New York Branch)

Abstract:
Estimating default probabilities of companies is one of the fundamental tasks in credit risk models and lending decision-making. One area of particular interest is how the companies’ asset value behaves in the presence of unforeseen external shocks or catastrophes. On one hand, we want the default probabilities to address the likelihood of catastrophes correctly, and on the other hand, we want to be able to perform what-if analysis to investigate the possible consequences of catastrophes. This study proposes a framework to perform such what-if analysis in the jump diffusion framework.

A Spot Pricing Framework to Enable Pricing and Risk Management of Inter-Domain Assured Bandwidth Services
Mehdi Aboulfadl, Aparna Gupta, Ritesh Pradhan, and Shivkumar Kalyanaraman (Rensselaer Polytechnic Institute)

Abstract:
In the current bandwidth market, Internet Service Providers (ISPs) provide guaranteed Internet bandwidth within their domains. However, they are incapable of providing such assurances for data crossing their domain boundaries. In this paper, we present a spot pricing scheme for Internet bandwidth contracts within an ISP domain. These models when implemented at access or exchange points of different ISP domains would provide assured bandwidth for inter-domain traffic. Each contract will constitute a Quality of Service agreement between a customer and a provider within an ISP domain. By appropriately bundling derivative contracts defined on the intra-domain service contracts, a provider will not only be able to give inter-domain Quality of Service assurance, but will be able to add new services and manage its portfolio of services.

Modeling Growth Stocks (Part II)
Samuel Kou (Harvard University) and Steve Kou (Columbia University)

Abstract:
Continuing the previous work on growth stocks, we propose a diffusion model for growth stocks. Since growth stocks tend to have low or even negative earnings and high volatility, it is a great challenge to derive a meaningful mathematical model within the traditional valuation framework. The diffusion model not only has economic interpretations for its parameters, but also leads to some interesting economic insight - the model postulates mean reversion (with a high mean reverting level) for growth stocks, which could be useful in understanding the recent boom and burst of the "internet bubble". Simulation and an empirical evaluation of the model based on the size distribution are also presented. The simulation and numerical results are quite encouraging.

Decision Aids for Scheduling and Hedging (DASH) in Deregulated Electricity Markets: A Stochastic Programming Approach to Power Portfolio Optimization
Suvrajeet Sen, Lihua Yu, and Talat Genc (University of Arizona)

Abstract:
The DASH model for Power Portfolio Optimization provides a tool which helps decision-makers coordinate production decisions with opportunities in the wholesale power market. The methodology is based on a stochastic programming model which selects portfolio positions that perform well on a variety of scenarios generated through statistical modeling and optimization. When compared with a commonly used fixed-mix policy, our experiments demonstrate that the DASH model provides significant advantages over several fixed-mix policies.

Crystal Ball Professional Introductory Tutorial
Lawrence I. Goldman (Decisioneering, Inc.)

Abstract:
Crystal Ball 2000 Professional Edition is a suite of easy-to-use Microsoft Excel add-in software that helps you analyze the risks and uncertainties associated with your spreadsheet models. The suite includes analysis tools for Monte Carlo simulation (Crystal Ball), time-series forecasting (CB Predictor), and optimization (OptQuest) as well as developer kits for building custom interfaces and processes. Spreadsheets alone are inadequate for assessing the probability of an event because they lack the ability to generate and analyze alternative scenarios in a sophisticated way. Spreadsheet add-ins such as Crystal Ball can provide this functionality and help modelers gain new insights into the mechanisms that drive their models and affect positive outcomes. This tutorial uses the example of an emerging media product to discuss how the analytical tools of Monte Carlo simulation and time-series forecasting can provide a greater understanding and quantification of the risks inherent in a spreadsheet-based business decision.

Portfolio Optimization for Capital Investment Projects
Jay April, Fred Glover, and James Kelly (OptTek Systems, Inc.)

Abstract:
The new portfolio optimization engine, OptFolio™, simultaneously addresses financial return goals, catastrophic loss avoidance, and performance probability. The innovations embedded in OptFolio enable users to confidently design effective plans for achieving financial goals, employing accurate analysis based on real data. Traditional analysis and prediction methods are based on mean variance analysis - an approach known to be faulty. OptFolio takes a much more sophisticated and strategic direction. State-of-the-art technology integrates optimization and simulation 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. OptFolio is currently being used to optimize project portfolio performance in oil and gas applications and in capital allocation and budgeting for investments in technology.

Optimal Active Management Fees
Jakša Cvitanic (University of Southern California) and Lionel Martellini and Fernando Zapatero (USC)

Abstract:
We consider the problem of a mutual fund manager that maximizes the present value of expected fees and has to decide the level of fee to impose on the fund. The fee will be paid by a risk averse investor that maximizes expected utility over final wealth. This investor can invest either in an indexed fund or in a managed fund. The manager has superior ability and, as a result of it, the fund offers a higher expected return. However, the investor has incomplete information about the ability of the fund manager. The investor has priors about this ability that are upgraded according to the performance of the fund. At some optimal level, the investor decides to switch from the market portfolio to the mutual fund. Our problem does not have a closed form solution, but we can compute optimal fees, using simulation.

Convergence of the Stochastic Mesh Estimator for Pricing American Options
Athanassios N. Avramidis (University of Montreal) and Heinrich Matzinger (Universtity of Bielefeld )

Abstract:
Broadie and Glasserman proposed a simulation-based method they named stochastic mesh for pricing high-dimensional American options. Based on simulated states of the assets underlying the option at each exercise opportunity, the method produces an estimator of the option value at each sampled state. Under the mild assumption of the finiteness of certain moments, we derive an asymptotic upper bound on the probability of error of the mesh estimator, where both the error size and the probability bound vanish as the sample size increases. We include the empirical performance for the test problems used by Broadie and Glasserman in a recent unpublished manuscript. We find that the mesh estimator has large bias that decays very slowly with the sample size, suggesting that in applications it will most likely be necessary to employ bias and/or variance reduction techniques.

Security Price Dynamics and Simulation in Financial Engineering
Stewart Mayhew (University of Georgia)

Abstract:
Applications in financial engineering have relied heavily on Brownian Motion as a workhorse model for pricing derivative securities and implementing risk management programs. When more than one state variable is required, the standard approach is to use a multivariate Brownian Motion with constant correlations. This article briefly summarizes several important reasons why this approach is not adequate (and in some cases, can lead to disaster). Examples include fat tails, volatility clustering, large discrete jumps, parameter instability, and asymmetric correlations. Including such features makes analytic modeling less tractable, and potentially makes simulation a more attractive alternative.

Using Computer Simulation to Mitigate Risk in Electricity Generation/Consumption Collaboration Policies
Thomas F. Brady (Purdue University North Central)

Abstract:
The electric utility industry has undergone fundamental change in the last decade. Foremost of these changes have been numerous deregulation attempts. Producers and large consumers have built business models based upon large volume transactions, which lead to smooth production and volume discounting. The risks associated with using these traditional business models in deregulated markets are many. This paper describes the development of a computer simulation environment that models a novel collaborative strategy proposed by a local electricity utility to mitigate highly varying load situations demanded by the largest steel-producing region in the United States. Through the use of this model, collaborative strategies for effective electricity generation and usage are developed and analyzed.

Batting Average: A Composite Measure of Risk for Assessing Product Differentiation in a Simulation Model
Daniel M. Hamblin (Dan Hamblin & Associates, Inc.) and Brian T. Ratchford (University of Maryland)

Abstract:
The paper simulates how market power affects electricity retailing to households. A pseudo-random number seeding algorithm creates representative product differentiation in repeated drawings, for an incumbent and seven challengers. A ninth player competitor decides how to distinguish her product. The simulation creates an efficient starting market, adjusted for competitor dominance; and, over a 12-month horizon, uses topology to develop unexploited profit opportunities for all competitors. A best solution criterion punishes nonconformists. Results of repeated drawings varying opposition to the player's constant product differentiation feed a batting average risk assessment. Decision rules reward hits based on profit and year's end market share. The market simulation tool supports conjectural assessment of social policy - household direct access to wholesale power, incentive for product differentiation versus that for mergers and acquisitions, and allocation of deregulation benefits to shareholders versus ratepayers.

Discrete Event Simulation for the Risk of Development of an Oil Field
Carlos Magno C. Jacinto (PETROBRAS SA)

Abstract:
The present work focuses on the development of a simulation method which provides an engineering tool for managing the risks associated with the development of an oil field. The developed method consists of performing discrete simulation based on data from field operations. The paper reports and discusses the simulation results of a real field development which lead to the following highlights: (1) the operations that present the highest level of risk are emphasized and studied for defining their impact on costs, (2) the consequences of some deviations from the pre-planned schedule are evaluated in terms of increasing the total amount of the investment, and (3) the possible gains and risks associated with the use of some emerging technologies are analyzed. This study shows that this methodology is an useful tool for providing relevant information to contracts negotiation with suppliers and drilling contractors.

Hedging Beyond Duration and Convexity
Jian Chen (Fannie Mae) and Michael C. Fu (University of Maryland)

Abstract:
Hedging of fixed income securities remains one of the most challenging problems faced by financial institutions. The predominantly used measures of duration and convexity do not completely capture the interest rate risks borne by the holder of these securities. Using historical data for the entire yield curve, we perform a principal components analysis and find that the first four factors capture over 99.99% of the yield curve variation. Incorporating these factors into the pricing of arbitrary fixed income securities via Monte Carlo simulation, we derive perturbation analysis (PA) estimators for the price sensitivities with respect to the factors. Computational results for mortgage-backed securities (MBS) indicate that using these sensitivity measures in hedging provides far more protection against interest risk exposure than the conventional measures of duration and convexity.

Effect of Implementation Time on Real Options Valuation
Harriet Black Nembhard, Leyuan Shi, and Mehmet Aktan (University of Wisconsin-Madison)

Abstract:
Exercising real options often requires an implementation time, whereas financial options can be exercised instantly. Neglecting the implementation time needed to exercise a real option causes overvaluing that option. We develop lattice and Monte Carlo simulation techniques to value real option problems, where exercising the option requires an implementation time. We present the application of the proposed techniques on a global supply chain network problem with exchange rate uncertainty and value the flexibility to switch between manufacturing options for a firm that has operations in different countries.

An Empirical Evaluation of Sampling Methods in Risk Analysis Simulation: Quasi-Monte Carlo, Descriptive Sampling, and Latin Hypercube Sampling
Eduardo Saliby (COPPEAD-UFRJ) and Flavio Pacheco (Banco Boreal de Investimentos S/A)

Abstract:
This paper compares the performance, in terms of convergence rates and precision of the estimates, for six Monte Carlo Simulation sampling methods: Quasi-Monte Carlo using Halton, Sobol, and Faure numeric sequences; Descriptive Sampling, based on the use of deterministic sets and Latin Hypercube Sampling, based on stratified numerical sets. Those methods are compared to the classical Monte Carlo. The comparison was made for two basic risky applications: the first one evaluates the risk in a decision making process when launching a new product; the second evaluates the risk of accomplishing an expected rate of return in a correlated stock portfolio. Descriptive sampling and Latin Hypercube sampling have shown the best aggregate results.