The first type measures the sensitivities of portfolio value to some particular market variables. Usually, a portfolio’s risk profile can be described by a large number of those sensitivities. The second type is more comprehensive as it calculates the probability distribution of the portfolio value at a given horizon. This then provides com¬mon risk measures that summarise the portfolio risk, such as value at risk (VaR).
Among the commonly applied methods to estimate VaR, the simplest is “delta approximation”. The method, however, depends on two assumptions: the normality assumption of portfolio value, and the linearity assumption of the relationship between transactions’ prices and market variables. For most portfolios, especially for portfolios with options and/or embedded options, Monte Carlo simulation is an appropriate method. The difficulty with the Monte Carlo approach is its computational burden.
The scenario simulation method described here is a computationally efficient alternative to conventional Monte Carlo for multicurrency fixed-income portfolios.
Scenario simulation provides the entire distribution of future portfolio returns. From this, not only VaR, but standard deviation and other measures of risk, such as the “coherent mea¬sures of risk”, can be computed. The scenario simulation model can be applied in estimating a portfolio’s overall risk profile of joint market and credit risks.
The scenario simulation method makes the simulation computationally practical for very large multicurrency portfolios of fixed-income securities and derivatives.
Applications to Value-at-Risk estimation and stress testing
The scenario simulation model provides an effective alternative to the delta approximation method and the traditional Monte Carlo method. We can directly apply the model by valuing each transaction and obtain the portfolio’s profit and loss distribution, and with it, the portfolio risk exposure statistics.
The scenario simulation model can also be applied to perform stress testing. VaR analysis is usually supplemented by stress testing, using the data from extraordinary historical market events. It is also important to stress test the assumptions of VaR mod¬els such as volatilities and correlations. Because of its computational efficiency, scenario simulation method is particularly suitable for such testing. In particular, the method allows risk managers to examine a portfolio’s risk exposures within the tail of a given distribution and to identify specific stress scenarios under which the portfolio may become vulnerable.
Applications to portfolio’s credit risk exposure estimation
There are three basic ingredients that go into estimating a portfolio’s potential credit risk:
1) market value of bonds and transactions for each issuer/counterparty;
2) the probability distribution of issuer or counterparty defaults;
3) the recovery rate distribution.
A portfolio will suffer a credit loss if an issuer or a counterparty defaults, the market value of the portfolio with respect to the issuer or the counterparty is positive, and the recovery rate is less than 100 percent.
Estimating credit risk is related to, but more complicated than, market risk estimation. All the above three ingredients are random, and they are usually correlated with each other. Unlike market risk management where the horizon is usually short credit risk management looks at much longer horizons, often the entire life of a transaction.
The scenario simulation model can be applied to estimate a portfolio’s credit risk exposure as well as its joint market and credit risk exposure.
This article is an edited version of
an entry in the “Encyclopedia of Quantitative Risk Analysis and
Assessment”, Copyright © 2008 John Wiley & Sons Ltd. Used by
permission.
