文档介绍：Value at Risk Chapter 16
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
The Question Being Asked in VaR
“What loss level is such that we are X% confident it will not be exceeded in N business days?”
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
VaR and Regulatory Capital
Regulators base the capital they require banks to keep on VaR
The market-risk capital is k times the 10-day 99% VaR where k is at least
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
VaR vs. C-VaR (See Figures and )
VaR is the loss level that will not be exceeded with a specified probability
C-VaR is the expected loss given that the loss is greater than the VaR level
Although C-VaR is theoretically more appealing, it is not widely used
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Advantages of VaR
It captures an important aspect of risk
in a single number
It is easy to understand
It asks the simple question: “How bad can things get?”
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Time Horizon
Instead of calculating the 10-day, 99% VaR directly analysts usually calculate a 1-day 99% VaR and assume
This is exactly true when portfolio changes on essive e from independent identically distributed normal distributions
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Historical Simulation (See Table and )
Create a database of the daily movements in all market variables.
The first simulation trial assumes that the percentage changes in all market variables are as on the first day
The second simulation trial assumes that the percentage changes in all market variables are as on the second day
and so on
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Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull
Historical Simulation continued
Suppose we use m days of historical data
Let vi be the value