Question

You have an outstanding fixed-for-fixed NOK/NZD swap for NOK 100 million, based on a historic spot rate of NOK/NZD 4 and initial seven-year swap rates of 7% (NZD, outflow) and 8% (NOK, inflow). The swap now has three years to go, and the current rates at NOK/NZD 4.5, 6% p.a. (NZD three years), and 5% p.a. (NOK three years). What is the market value of the swap contract in NOK?

Answer 1

First we have to calculate the Present value of leg1( inflow of NOK interest i.e. 8% of 100m = 8m) @ current market rate which is 5% for NOK. Note that we won't consider the notional cashflow of 100m$ since it won't be actually exchanged.

Hence PV of inflow leg = 8/1.05 +8/(1.05)^2 +8/(1.05)^3 =21.79 million NOK

Now lets come to the leg 2

The notional equivalent NZD principal should be 100/4 = 25 million because initial exchange rate was 4 nok/nzd i.e. 100m nok was exchanged for 25m nzd

Similarly we can calculate the PV if leg 2 ( outflows of NZD interest i.e. 7% of 25m =1.75m) @current market rate 6%

So PV of outflow leg = 1.75/1.06 +1.75/(1.06)^2 +1.75/(1.06)^3 = 4.68 million NZD

Now since we want the swap value in NOK ,we have to convert NZD in nok at current spot rate. Which is 4.5 NOK/NZD

So PV of outflows leg inNOK is= 4.68 NZD × 4.5 = 21.06 million NOK

So net market value of swap for the party who receives NOK is PV of inflows in NOK - PV of NOK outflows = 21.79 -21.06 =.73 million i.e. swap is in the favour of this party.