We have now learned about how VaR can be calculated for primitive positions including spot FX positions, equity positions, zero-coupon bonds, and futures/forward positions. We will now look at how complex positions can be decomposed into these primitive instruments which are mapped to risk factors.

In this article we will take a look at some of these complex positions.

**Coupon Paying Bonds:** A coupon paying bond can be looked at as a portfolio of zero-coupon instruments (Think each coupon payment as a zero-coupon bond). The VaR of the coupon bond will be calculated based on the VaR of the mapped equivalents of zero-coupon cash flows at benchmark maturities. See Mapping Zero-coupon Bonds.

**Forward Rate Agreement**:** **Forward Rate Agreements (FRA’s) are similar to forward contracts where one party agrees to borrow or lend a certain amount of money at a fixed rate on a pre-specified future date. It’s an exchange of a single floating amount for a single fixed amount at a given future date. The payoff from the floating leg of the FRA can be regarded as a portfolio of two zero-coupon bonds. One long position in the zero-coupon bond maturing at the end of FRA and a short position in a zero-coupon bond maturing at beginning of FRA period, both bonds having same face value and notional principal. The VaR of the FRA will then be the VaR of the portfolio of these two zero-coupon bonds. See Mapping Zero-coupon Bonds.

**Floating Rate Notes:** Floating rate notes (FRNs) have variable coupons and the coupon is reset at the beginning of the coupon period. A floating rate note has the same sensitivity as a zero-coupon bond with maturity equal to the reset interval, and is often regarded as essentially immune to interest rate risk. Therefore, the VaR of an FRN can be calculated as if it’s a zero-coupon bond that matures on the next coupon date. See Mapping Zero-coupon Bonds.

**Vanilla Interest rate Swaps:** An interest rate swap can be looked at as a portfolio of a long position in a fixed-coupon bond and a short position in a floating rate bond, which are mapped to zero-coupon bonds as seen above.

**Structured Notes: **A structured note can be treated as a portfolio of interest-rate swaps and floating rate notes.

**FX Forwards:** This is a combination of a long position in foreign currency zero-coupon bond and a short position in domestic zero-coupon bond.

Similarly any complex position can be broken down into a combination of the four primitive instruments.

## Leave a Reply