- CFA Exams
- CFA Level I Exam
- Study Session 14. Derivatives
- Reading 38. Valuation of Contingent Claims
- Subject 5. Black Option Valuation Model
CFA Practice Question
Consider a European payer swaption that expires in two years and is exercisable as a one-year swap with quarterly payments, using 90/360 as the day-count adjustment. The exercise rate is 3.6%. The notional principal is $20 million. Now suppose we are at the swaption expiration and the term structure is as follows:
What is the value of the swaption right before expiration?
A. $15,643
B. $4,000
C. $184,000
Explanation: Under these conditions, the swap fixed payment should be 0.0092, equating to an annual fixed rate of 3.68%. The holder of the swaption has the right to enter into a swap to pay 3.6% (which corresponds to a quarterly payment of $180,000), whereas in the market such a swap would require payment at a rate of 3.68% (which corresponds to a quarterly payment of $184,000). If the holder exercises the swap, and enters an opposite swap in the market, he effectively receives a net quarterly payment stream of $184,000 - $180,000 = $4,000. The present value of this payment stream is $4,000 (0.9914 + 0.9824 + 0.9730 + 0.9639) = $15,643.
User Contributed Comments 12
| User | Comment |
|---|---|
| danlan2 | Where does 3.68% come from? |
| danlan2 | 3.68%=sum of all discount factor =0.9914+0.9824+0.9730+0.9639 |
| frankal101 | no it does not... |
| ThePessimist | (360/90)*(1-0.9639)/(sum of discount factors)=3.68% |
| ReeM | 1-Z4/(Z1+Z2+Z3+Z4) |
| DZ2008 | Your calculations are incorrect. Doing what you said results in 3.6924%. (360/90)*(1-0.9639)/(.9914+.9824+.973+.9639)=3.6924% actually carry out the calculations and you will see, 3.68% is a mystery |
| DZ2008 | Ahhh I see ... they rounded to 0.0092 for this part: (1-0.9639)/(.9914+.9824+.973+.9639) even though it should actually be 0.009231, which makes a big difference |
| dblueroom | Yep, if you had 3.6924, you would end up with 17,000 + I used 3.069% |
| HectorRS2 | Rat diff: 3.68% - 3.60%=.08% Annualized to quaterly: .08% * 90/360 = .02% Quaterly Payment: .02% * 20.000.000= 4.000 PV =4.000*(discount factors) =15.643 |
| uviolet | ThePessimist is correct. Use the Fixed rate formula and then multiply it by 4 to get the annual rate of 3.68 |
| broadex | Calculate Fixed Rate: x/4(sum of discounts)=1 (i.e variable reset of 1) x=3.69% Then calculate rate diff: 0.08% |
| adamrej | If you do things carefully, the market rate you find is 3.69(...) and not 3.68. This little (seemingly inconsequential) difference makes the PV of swaption to be about $17600 about $2000 off the answer provided. |