## Var & Swap position

balajismz
Finance Junkie
Posts: 63
Joined: Mon Nov 05, 2012 9:13 am

### Var & Swap position

Consider a position in a 5 year receive fixed swap that makes annual payments on a USD 100 million notional. The floating leg has just been reset. The term structure is flat at 5%, the Macaulay duration of a 5?year par bond is 4.5 years, and the annual volatility of yield changes is 100bp. Your best estimate of the swap’s VaR with 95% confidence over the next month is:
a. USD 7.1 million
b. USD 5.5 million
c. USD 1.6 million
d. USD 2.0 million

Because the floating-rate leg has just been reset, its duration is 1. Net duration is 4.5-1=3.5 year, or modified duration of 3.5/1.05=3.33. The 95% VaR of monthly changes in yields is 1.65*1%*5%/sq root (12) = 0.023%. Multiplying, this gives USD 100*0.023%*3.33=USD 0.079

But the ans as per prestine is C 1.6Mn

Can someone try this??

Balaji

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vandana.jain
Finance Junkie
Posts: 41
Joined: Tue Jul 24, 2012 4:56 pm

### Re: Var & Swap position

I think here we should take 1% as a sd not 5%.
then ans would be @ 1.58...

balajismz
Finance Junkie
Posts: 63
Joined: Mon Nov 05, 2012 9:13 am

### Re: Var & Swap position

Well, here we need to consider the volatility of yield, yield and modifield duration along with Z value and Principal Value

Balaji