Value of a Swap to the USD payer?

CFA Level II Derivatives
#1

Hi team,

The below question comes from the Kaplan Schweser question bank. I see the answer provided and how they got there, but the process seems not at all logical or elegant. I would love to see an alternative calculation method.

Consider a fixed-for-fixed 1-year $100,000 semiannual currency swap with rates of 5.0% in USD and 4.8% in CHF, originated when the exchange rate is $0.34. After the first settlement, the exchange rate is $0.35 and the term structure is:

90 Days

LIBOR: 5.2%

Swiss: 4.8%

180 days

LIBOR: 5.6%

Swiss: 5.4%

What is the value of the swap to the USD payer?

Thanks in advance :slight_smile:

#2

I have obviously missed the mark with forum etiquette, my apologies.

Can someone kindly advise what is wrong with the question or the way it is asked?

#3

Value of the swap to the USD payer ( receive CHF; pay USD ) = Value of CHF leg - Value of USD leg

USD Notional = $100,000

CHF Notional = $100,000 / $0.34 = CHF 294,118 (based on CHF 1 = $0.34)

Semi-annual payment in USD = $100,000 x 5%/2 = $2,500

Semi-annual payment in CHF = CHF 294,118 x 4.8%/2 = CHF 7,058.832

After the first settlement (at t = 180), there is only one payment left (interest + notional) in 180 days time (t = 360).

PV(USD payments) = ($2,500 + $100,000)/(1 + 0.056 x 180/360) = $99,708.17

PV(CHF payments) = (CHF 7,058.83 + CHF 294,118)/(1 + 0.054 x 180/360) = CHF 293,258.84

The last step is to convert to a common currency for the payments (this depends on the options given in the question; whether it is in USD or CHF).

In USD terms , the value of the swap to the USD payer is:

(CHF 293,258.84 x 0.35) - $99,708.17 = $102,640.59 - $99,708.17 = $2,932.42

In CHF terms , the value of the swap to the USD payer is:

CHF 293,258.84 - ($99,708.17 / $0.35) = CHF 293,258.84 - CHF 284,880.49 = CHF 8,378.35

1 Like
#4

Thank you very much. You really did an excellent job in resolving this question. As @jim8z3 mentioned, Schweser question bank made an uneasy explanation and I lost too. Your solution is crystal.