eprintid: 172
rev_number: 4
eprint_status: archive
userid: 6
dir: disk0/00/00/01/72
datestamp: 2008-10-10
lastmod: 2015-05-29 19:48:40
status_changed: 2009-04-08 16:55:17
type: report
metadata_visibility: show
item_issues_count: 0
creators_name: Kane, Selly
creators_name: Krupp, Viktoria
creators_name: Macki, Jack
contributors_name: Chadam, John
contributors_name: Hanson, Joel
contributors_name: Kazmerchuk, Yuriy
contributors_name: Kreinin, Alex
contributors_name: Hsu, Victoria
contributors_name: Machorro, Eric
contributors_name: Masum, Hassan
contributors_name: Mahammadalikhan, Ramin
contributors_name: Saxena, Barkha
contributors_name: Sun, LiMei
contributors_name: Meza, Rafael
title: Monte Carlo Simulation in the Integrated Market and Credit Portfolio Model
ispublished: pub
subjects: finance
studygroups: ipsw5
companyname: Algorithmics
full_text_status: public
abstract: Credit granting institutions deal with large portfolios of assets. These assets represent credit granted to obligors as well as investments in securities. A common size for such a portfolio lies from anywhere between 400 to 10,000 instruments.

The essential goal of the credit institution is to minimize their losses due to default. By default we mean any event causing an asset to stop producing income. This can be the closure of a stock as well as the inability of an obligor to pay their debt, or even an obligor's decision to pay out all his debt.

Minimizing the combined losses of a credit portfolio is not a deterministic problem with one clean solution. The large number of factors influencing each obligor, different market sectors, their interactions and trends, etc. are more commonly dealt with in terms of statistical measures. Such include the expectation of return and the volatility of each asset associated with a given time horizon.

In this sense, we consider in the following the expected loss and risk associated with the assets in a credit portfolio over a given time horizon of (typically) 10 to 30 years. We use a Monte Carlo approach to simulate the loss of a portfolio in multiple scenarios, which leads to a distribution function for the expected loss of the portfolio over that time horizon. Second, we compare the results of the simulation to a Gaussian approximation obtained via the Lindeberg-Feller Theorem. Consistent with our expectations, the Gaussian approximation compares well with a Monte Carlo simulation in case of a portfolio of very risky assets.

Using a model which produces a distribution of expected losses allows credit institutions to estimate their maximum expected loss with a certain confidence interval. This in turn helps in taking important decisions about whether to grant credit to an obligor, to exercise options or otherwise take advantage of sophisticated securities to minimize losses. Ultimately, this leads to the process of credit risk management.
problem_statement: Estimation of the risk involved in large portfolios of securities posing various individual credit risks is a problem which can be studied using Monte Carlo methods. The main difficulties include

1. the large number of different risk factors (interest rates, foreign exchange rates, ...)

2. statistical dependencies between market risk factors and probabilities of default.

There are several variance reduction techniques (importance sampling, stratified sampling, ...) which are applicable to many practical problems in finance, in particular to the pricing of sophisticated securities. The problem we face is how to utilize these techniques for portfolio risk analysis.

In general, the problem can be considered in both one-time-step and multi-time-step settings. The most interesting practical case corresponds to non-risky credit portfolios. In this case the portfolio losses depend on default events that are relatively rare. Therefore, efficient Monte Carlo simulation could be based on a transformation of the measure describing the joint evolution of market and credit risk factors.

A framework for credit risk estimation that has been used in industry is based on a joint market credit risk model described by Idcoe, Kreinin and Rosen.
date: 2001
date_type: published
pages: 18
citation:   Kane, Selly and Krupp, Viktoria and Macki, Jack  (2001) Monte Carlo Simulation in the Integrated Market and Credit Portfolio Model.  [Study Group Report]     
document_url: http://miis.maths.ox.ac.uk/miis/172/1/algorithmics.pdf