Value at Risk for Derivative Instruments
Value at Risk (VaR) has become a cornerstone of risk management in financial institutions. It is particularly interesting when dealing with derivative instruments. This article explains VaR in simple terms and its specific application to derivatives.
What is Value at Risk?
Value at Risk answers a simple yet crucial question: "How much could we lose on our investment over a specific time period, with a certain level of confidence?" For example, a one-day 95% VaR of $1 million means there's a 95% chance that the portfolio won't lose more than $1 million in a single day.
Why VaR is Different for Derivatives
Derivatives present unique challenges for VaR calculations because:
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Non-linear Behavior: Unlike stocks or bonds, many derivatives don't move in a straight line with their underlying assets. Options, for instance, can show dramatically different price changes depending on market conditions.
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Time Decay: Some derivatives, particularly options, lose value over time even if nothing else changes in the market.
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Multiple Risk Factors: A single derivative might be affected by various factors like interest rates, volatility, and the price of the underlying asset.
Main Approaches to Calculate VaR for Derivatives
1. Historical Simulation Method
This approach uses actual historical data to estimate potential future losses. For derivatives, we:
- Collect historical price changes of the underlying assets
- Apply these changes to current positions
- Calculate the derivative's value for each scenario
- Sort the results to find the VaR at the desired confidence level
The formula for historical VaR at confidence level α is:
