Pricing a currency swap. The currencies involved in the swap are USD and EUR. Th
ID: 2815139 • Letter: P
Question
Pricing a currency swap. The currencies involved in the swap are USD and EUR. The maturity of the swap is 3 years and the swap pays every year. The swap rate of the USD leg is 4% while the swap rate of the EUR leg is 5%. The nominal for the USD leg is 80 while the nominal for the EUR leg is 100. The zero rate curve (CC) for the USD currency is flat at 4.2% while for the EUR it is flat at 5.4%. The spot exchange rate is 1EUR = 0.85USD.
Compute the value of the swap paying the USD leg and receiving the EUR leg. The value will expressed in EUR.
Explanation / Answer
Value of a Swap is the difference in present value of the two cashflows. For example in case of an interest rate swap, paying fixed rate in exchange of floating
Value of Swap = Bflt - Bfix
In case of currency swaps however present values of cashflows need to be expressed in same currency hence
Value of Currency Swap = BEUR - BUSD x Spot Exchange Rate
Step 1 Calculation of Present Value of Cashflows
Following Table shows how to calculate present value -
a. First calculate discount factor using the excel formula "=1/POWER(1.042,1)". Here 0.042 is Zero Rate for USD.
b. Determine cashflows. This Swap will pay annually for next three years, using swap rate for respective leg as well as nominal value we determine the cashflows. For example cashflow in year 1 for USD leg would be Swap Rate USD leg*Nominal for USD. In third year cash flow would be principal + interest.
c. Calculate present value for cashflow by multiplying discount factor to cashflow.
d. Add the present values to get present value of each leg.
Step 2. Value of Swap in Euro
Discount factor USD Discount factor (EUR) PV CF(USD) PV CF (EUR) T rT (USD) rT(EUR) CF(USD) CF(EUR) 1 0.042 0.959692898 0.054 0.948766603 3.2 3.0710173 5 4.743833 2 0.042 0.921010459 0.054 0.900158068 3.2 2.9472335 5 4.50079 3 0.042 0.883887197 0.054 0.854039912 83.2 73.539415 105 89.67419 PV USD leg 79.557666 PV EUR leg 98.91881Related Questions
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