Mapping Spot FX Positions
In the previous article, we learned the need for VaR Mapping, and how financial instruments can be broken down into simpler building blocks/primitive instruments, which are mapped to a small set of risk factors.
One such building block instrument is spot FX positions, where you hold a foreign currency instrument whose value is fixed in terms of the foreign currency.
The mapping system of the financial institution will have a set of core currencies for which various historical and estimated data such as volatilities and correlations will already be available in the system.
If our FX position is based on one of these core currencies then our work is even easier. However, if our position is on a currency not from this core currency list, then we will have derive a proxy of our position in terms of one of the core currencies.
Assuming the exchange rates follow a normal distribution, the VaR of an FX spot position will be calculated as follows:
VaR = -Zα * σx * P * X
- P is the value of our position if foreign currency units
- X is the exchange rate
Let’s say that you have an FX spot position of EUR10,000,000 and the domestic currency is USD. Exchange rate is 1 EUR = 1.23 USD.
The estimated volatility is 20%.
As 99% confidence level, the daily VaR for this position will be:
VaR = -2.32635 * 0.20/Sqrt(250) * 12,300,000
\= USD 361,943
This method can be applied to other spot positions also, such as commodities.