Page 181 - DMGT513_DERIVATIVES_AND_RISK_MANAGEMENT

Derivatives & Risk Management

Notes
Figure 13.2

Self Assessment

Fill in the blanks:
6. Value at Risk (VaR) is a market risk measurement approach that uses ………….. market
trends.

7. …………. is a statistical methodology that helps risk managers to aggregate risk numbers
across business and product lines in a meaningful way.
8. VaR measures the largest loss likely to be suffered on a portfolio or a position over a
holding period (usually 1 to 10 days) with a given …………….. (confidence level).

13.3 Historical Simulation

Historical simulations represent the simplest way of estimating the Value at Risk for many
portfolios. In this approach, the VaR for a portfolio is estimated by creating a hypothetical time
series of returns on that portfolio, obtained by running the portfolio through actual historical
data and computing the changes that would have occurred in each period.
To run a historical simulation, we begin with time series data on each market risk factor, just as
we would for the variance-covariance approach. However, we do not use the data to estimate
variances and covariances looking forward, since the changes in the portfolio over time yield all
the information you need to compute the Value at Risk. Cabedo and Moya provide a simple
example of the application of historical simulation to measure the Value at Risk in oil prices.
Using historical data from 1992 to 1998, they obtained the daily prices in Brent Crude Oil and
graphed out the prices in Figure 13.3.
They separated the daily price changes into positive and negative numbers, and analyzed each
group. With a 99% confidence interval, the positive VaR was defined as the price change in the
99th percentile of the positive price changes and the negative VaR as the price change at the 99th
percentile of the negative price changes. For the period they studied, the daily Value at Risk at
the 99th percentile was about 1% in both directions.

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