- CFA Exams
- CFA Exam: Level II 2021
- 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 receiver 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

_{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?

Correct Answer: $1,184,681

B

B

B

B

First we compute the present value discount factors:

B

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

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

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

_{0}(360) = 1 / (1 + 0.0538 (360/360)) = 0.9489The fixed rate should be: 1/(90/360) x (1 - 0.9489) / (0.9908 + 0.9790 + 0.9655 + 0.9489) = 0.0528.

The market value at expiration of the receiver swaption is Max {0, [0.065 x (90/360) - 0.0528 x (90/360)] x (0.9908 + 0.9790 + 0.9655 + 0.9489)} = 0.01184681.

Based on notional principal of $100 million, the market value is $100,000,000 x 0.01184681 = $1,184,681.

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