CFA Practice Question

There are 227 practice questions for this study session.

CFA Practice Question

Consider a European payer swaption that expires in two years and is on a one-year swap that will make quarterly payments. The swaption has an exercise rate of 6.5%. The notional principal is $100 million. At expiration, the term structure of interest rates is as follows:
L0(90) = 0.0373; L0(180) = 0.0429; L0(270) = 0.0477; L0(360) = 0.0538.

What is the market value of the swaption at expiration?
A. $0
B. $1.2 million
C. $1.5 million
Explanation: First we compute the present value discount factors:
B0(90) = 1 / (1 + 0.0373 (90/360)) = 0.9908
B0(180) = 1 / (1 + 0.0429 (180/360)) = 0.9790
B0(270) = 1 / (1 + 0.0477 (270/360)) = 0.9655
B0(360) = 1 / (1 + 0.0538 (360/360)) = 0.9489

The fixed rate should be: 1/(90/360) x (1 - 0.9489) / (0.9908 + 0.9790 + 0.9655 + 0.9489) = 0.0528

The market value of the receiver swaption at expiration is Max {0, [0.0528 x (90/360) - 0.065 x (90/360)] x (0.9908 + 0.9790 + 0.9655 + 0.9489)} = 0.

User Contributed Comments 5

User Comment
americade the value of the swaption at expiration is like the call price over the contract rate that in this case is zero b/c the computed fixed is lower than contact so call price is zero
phadrian strike is higher than every single of the rates so pv must be 0
Paulvw Great answer, phadrian! I could have saved myself a lot of time.
shajidubai In qn it was mentioned payer swaption an used the correct formula, but mentioned as receiver swaption in answer
soorajiyer Phadrian, thats brilliant stuff. thanks mate!
You need to log in first to add your comment.