In most cases IM is re-calculated daily to reflect the changing composition of the portfolio, changing market conditions and daily updates to scenarios.
Methods of calculating IM include:
- Value at Risk (VaR) using historical simulation
- Value at Risk using Monte Carlo simulation
- Sensitivity mapping, such as used in the ISDA SIMM
A worked example
This example is using a historical simulation VaR, with a 5 day holding period and 100% confidence level.
- Create your list of scenarios. These are often the end of day prices for the assets in question
- Establish the starting price of the trade, in this case 100
- Calculate the change in values of the trade over a 5 day period.
- The day 5 value is 98, the day 1 price is 101, meaning a -3 move in prices over the 5 day period
- The trade is therefore worth 100-3 = 97
- Take the list of 5 day moves, and sort it, from biggest loss to biggest profit
- Take the biggest loss, in this case -97, this becomes your IM for todays calculation
- In a statistical sense, this is at the 100% confidence level, within the calculated results distribution. It doesn't mean you are "100% confident" that this is the worst loss that could ever occur in the real-world
- If you wanted to pick the 97% confidence level, you would pick the 30th item on the sorted list starting from the worst loss (in this theoretical example there are 1,000 scenarios)
- The 970th item from best profit is the same item as the 30th item from the worst loss