- CFA Exams
- CFA Level I Exam
- Study Session 14. Derivatives
- Reading 38. Valuation of Contingent Claims
- Subject 5. Black Option Valuation Model

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**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:

L

L

_{0}(90) = 0.0373; L_{0}(180) = 0.0429; L_{0}(270) = 0.0477; L_{0}(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:

B

_{0}(90) = 1 / (1 + 0.0373 (90/360)) = 0.9908

B

_{0}(180) = 1 / (1 + 0.0429 (180/360)) = 0.9790

B

_{0}(270) = 1 / (1 + 0.0477 (270/360)) = 0.9655

B

_{0}(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.

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**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! |