WSC 2005 Final Abstracts

The Delivery Option in Mortgage Backed Security Valuation Simulations
Scott Gregory Chastain and Jian Chen (Fannie Mae)

Abstract:
A delivery option exists in mortgage-backed security market, which has not been considered in existing mortgage pricing simulation literature. We explain the delivery option, the "To Be Announced" trade. We discuss how the presence of the delivery option effects the use of the standard pricing simulation technique. This technique uses a risk neutral interest rate simulation with a prepayment option model to recover a price which is an expectation over the possible rate outcomes. The simulation technique uses Monte Carlo integration with a suitable selected pseudo or quasi-random sequence. To recover market prices a spread term called the "Option Adjusted Spread" is required. We see that multiple simulations are required to explore the full structure of the delivery option but suggest how to use one simulation to approximate pricing even when the delivery option is present.

Simulation Analysis of Correlation and Credit Migration Models for Credit Portfolios
William J. Morokoff (Moody’s KMV)

Abstract:
The market for derivatives such as first-to-default baskets and CDO tranches on portfolios of corporate credit exposures (bonds, loans, default swaps, etc.) has grown rapidly in recent years. Various models for capturing portfolio correlation effects have been introduced, with Default Time models becoming the most widely used. While attractive for their relative simplicity and ability, in some cases, to allow fast computation of hedge ratios, there is increasing concern around the limitations and implications of these models. This paper uses simulation to study the effects of credit migration and correlation assumptions underlying the models for valuation of derivatives on credit portfolios.

A Loss Default Simulation Model of the Federal Bank Deposit Insurance Funds
Rosalind L. Bennett, Daniel A and Nuxoll (FDIC), Robert A. Jarrow (Cornell University) and Michael C. Fu and Huiju Zhang (University of Maryland)

Abstract:
This paper discusses a simulation model that is used in a martingale valuation approach to measure and value the risk of the FDIC deposit insurance funds. The FDIC insurance funds capitalize a portfolio of insurance policies, each issued to depositors of an individual commercial bank. To evaluate this portfolio, our methodology evaluates the insurance policies for depositors at each individual bank and aggregates to obtain the risk of the entire portfolio. To adequately model the risks associated with credit, interest rate, deposit growth, and loss rate, a multi-dimensional system is formulated. The risk measurement and valuation results are based on Monte Carlo simulation of the system risks.

Simulation of Risk and Return Profiles for Portfolios of CDO Tranches
William J. Morokoff (Moody's KMV)

Abstract:
Investments in Collateralized Debt Obligations (CDOs) often offer attractive yields relative to other similar debt instruments (corporate bonds, etc.). However, the risk profiles of CDO investments, and in particular portfolios of these investments, can be substantially different from straight credit portfolios due to complex correlation dependence across CDOs. Simulation is generally required to capture the intricate interaction of default and correlation risk that determines the risk and return profile of a portfolio of CDO investments. This paper considers some of the issues that must be addressed in determining the risk profiles with simulation and presents results on a simple example.

Expected Shortfall in Credit Portfolios with Extremal Dependence
Achal Bassamboo (Kellog School of Management), Sandeep Juneja (Tata Institute of Fundamental Research) and Assaf Zeevi (Columbia University)

Abstract:
We consider the risk of a portfolio comprised of loans, bonds, and financial instruments that are subject to possible default. We are interested in efficiently estimating expected excess loss conditioned on the event that the portfolio incurs large losses over a fixed time horizon; this risk measure is often referred to as expected shortfall. We consider a heterogeneous mix of obligors and assume a portfolio dependence structure that supports extremal dependence among obligors and does not hinge solely on correlation. We first derive sharp asymptotics that illustrate the implications of extremal dependence among obligors in the risk of the portfolio. Using this as a stepping stone, we develop a multi-stage importance sampling algorithm that is shown to have bounded relative error in estimating expected shortfall.

Fast Simulation of Multifactor Portfolio Credit Risk in the t-Copula Model
Wanmo Kang (Moody's KMV) and Perwez Shahabuddin (Columbia University)

Abstract:
We present an importance sampling procedure for the estimation of multifactor portfolio credit risk for the t-copula model, i.e, the case where the risk factors have the multivariate student t distribution. We use a version of the multivariate student t that can be expressed as a ratio of a multivariate normal and a scaled chi-square random variable. The procedure consists of two steps. First, using the large deviations result for the Gaussian model in Glasserman, Kang, and Shahabuddin (2005a), we devise and apply a change of measure to the chi-square random variable. Then, conditional on the chi-square random variable, we apply the importance sampling procedure developed for the Gaussian-copula model in Glasserman, Kang, Shahabuddin (2005b). We support our importance sampling procedure by numerical examples.

Out-of-the-money Monte Carlo Simulation Option Pricing: The Joint Use Of Importance Sampling And Descritptive Sampling
Eduardo Saliby, Jaqueline T.M. Marins, and Josete F. dos Santos (Coppead/UFRJ)

Abstract:
As in any Monte Carlo application, simulation option valuation produces imprecise estimates. In such an application, Descriptive Sampling (DS) has proven to be a powerful Variance Reduction Technique. However, this performance deteriorates as the probability of exercising an option decreases. In the case of out of the money options, the solution is to use Importance Sampling (IS). Following this track, the joint use of IS and DS is deserving of attention. Here, we evaluate and compare the benefits of using standard IS method with the joint use of IS and DS. We also investigate the influence of the problem dimensionality in the variance reduction achieved. Although the combination IS+DS showed gains over the standard IS implementation, the benefits in the case of out-of-the-money options were mainly due to the IS effect. On the other hand, the problem dimensionality did not affect the gains. Possible reasons for such results are discussed.

Function-approximation-based Perfect Control Variates for Pricing American Options
Sandeep Juneja and Nomesh Bolia (Tata Institute of Fundamental Research)

Abstract:
Monte Carlo simulation techniques that use function approximations have been successfully applied to approximately price multi-dimensional American options. However, for many pricing problems the time required to get accurate estimates can still be prohibitive, and this motivates the development of variance reduction techniques. In this paper, we describe a zero-variance or `perfect' control variate to price American options. We then discuss how function approximation may be used to approximate this perfect control variate. Empirically, we observe that on simple one dimensional examples, this approximately perfect control variate gives orders of magnitude of variance reduction compared to naive estimation.

A Study of Variance Reduction Techniques for American Option Pricing
Christiane Lemieux and Jennie La (University of Calgary)

Abstract:
American option pricing is a challenging problem in financial mathematics for which several approaches have been proposed in the last few years. In this paper, we consider the regression-based method of Longstaff and Schwartz (2001) to price these options, and then investigate the use of different variance reduction techniques to improve the efficiency of the Monte Carlo estimators thus obtained. The techniques considered have been shown to work well for European option pricing. One of them is importance sampling, in which the approach of Glasserman, Heidelberger and Shahabuddin (1999) is applied to find an appropriate change of measure. We also consider control variates and randomized quasi-Monte Carlo methods, and use numerical experiments on American Asian call options to investigate the performance of these methods.

Risk Assessment of Drilling and Completion Operations in Petroleum Wells Using a Monte Carlo and a Neural Network Approach
Dennis Kerr Coelho, Mauro Roisenberg, and Paulo José Freitas (Federal University of Santa Catarina) and Carlos Magno Jacinto (Petrobras)

Abstract:
This paper intends to show how two different methodologies, a Monte Carlo simulation method and a connectionist approach can be used to estimate the total time assessment in drilling and completion operations of oil wells in deep waters. The former approach performs a Monte Carlo simulation based on data from field operations. In the later one, correlations and regularities in parameters selected from a petroleum company database were detected using a competitive neural network, and then, a feedforward neural network was trained to estimate the average, standard deviation and total time wasted in the accomplishment of the well. At the end, the results obtained by both models are compared. The analyst could evaluate the precision of the estimated total-time based on geometric and technological parameters provided by the neural network tool, with those supplied by the traditional Monte Carlo method based on data of the drilling and completion operations

Identifying Demand Sources That Minimize Risk for a Selective Newsvendor
Kevin M. Taaffe and Deepak Tirumalasetty (Clemson University)

Abstract:
Consider a firm that offers a product during a single selling season. The firm has the flexibility of choosing which demand sources to serve, but these decisions must be made prior to knowing the actual demand that will materialize in each market. Moreover, we assume the firm operates on a tight budget and cannot afford to record several successive financial losses spanning consecutive periods. In this case, it is likely that their objective is not only to maximize expected profit, but to minimize the variance from that goal. We provide insights into the tradeoff between expected profit, expected revenue, and demand uncertainty. Finally, we present a solution approach, via simulation, to determine the best set of markets to pursue and the associated order quantity when the firm's objective is to minimize the probability of receiving a profit below a critical threshold value.

Using Simulation to Analyze R&D Value Creation
Douglas A. Bodner, William B. Rouse, and Michael J. Pennock (Georgia Institute of Technology)

Abstract:
As the front-end to product and system lifecycles, research and development activities serve as engines of value creation. By nature, though, R&D involves significant uncertainty. As such, it often is viewed as an investment problem, whereby funds are invested in ventures under risk, with the hope of achieving future value. This paper investigates the use of organizational simulation to analyze the R&D investment problem, focusing on ways to increase value created from R&D. Based on a process-focused model of R&D systems, initial results indicate that using a real options framework to valuate R&D outperforms traditional discounted cash flow (DCF) methods in total value created, but that DCF methods are preferred for return on R&D investment. To complement the process-focused R&D system model, a product-focused model of R&D is specified and integrated with the process-focused model.