Hi Guys
I’m really having difficulty grasping the concept behind Cross Currency Swaps and how to work out the valuations.
Can you please guide me through this question?
IMGUR link to q:
IMGUR link to answer:
The company makes payments in Yens. Over the year, it’ll pay 1.58% every quarter, followed by the face value at the end of the year. This translates to the following per unit of notional value: Q1: .0158 (which you multiply by the discount factor of .9912 to give .0157 PV Q2: .0158 (which you multiply by the discount factor of .981 to give .0155 PV Q3: .0158 (which you multiply by the discount factor of .9705 to give .0153 PV Q4: .0158 (which you multiply by the discount factor of .97 to give .0153 PV Q4: 1 (this is the face value upon maturity, which also gets multiplied by the .97 discount factor to give .97 PV Add up all the cashflows to give the total PV of the Yen cashflows = 1.0318. Since this is per notional amount, and total notional amount is 1 million, the total value is 1.0318 * 1m = 1,031,821 Yen. Convert this back to Pounds using the given exchange rate to give 1,031,821/125 = 8,255 Pounds. Next we look at the Pounds side of the story, where the rate is .235%. Set up the cashflows exactly like above, such that every quarter the company receives .00235 (discount these by the discount factors for each quarter), followed by 1 in the final period. Add up the PVs to give you .9691, which multiplied by the notional amount of 8,333 is 8,076. So in sum, the value of what the company pays is 8,255 pounds, and what it receives is 8,076. The difference is 179. Swaps are really hard for me too. Never encountered them before studying for lvl 2.
I just went through this, hopefully I can help.
Before you do anything realize that this is a fixed for fixed swap. Because the payments are settled quarterly you will be essentially finding the present value of 4 payments for each currency (The first 3 are interest only and the last payment is interest + principal). Once you have the sum of the present values for both sides, you’ll have to convert one side to the other currency by the given spot rate (125 Yen/GB) and net the two to get your answer. Ok that was how it’s done conceptually, below is with the numbers.
- Calculate the 4 quarterly payments on the Yen side
60 - (Yen notional) * (Yen fixed rate) * PVA = (1,000,000) * (.0158) * (.9912) = 15,660.96
150 - (Yen notional) * (Yen fixed rate) * PVA = (1,000,000) * (.0158) * (.9810) = 15,499.80
240 - (Yen notional) * (Yen fixed rate) * PVA = (1,000,000) * (.0158) * (.9705) = 15,333.90
330 - [(Yen notional) * (Yen fixed rate) + (Yen notional)] * PVA = [(1,000,000) * (.0158) + (1,000,000)] * (.9700) = 985,326
(note that the last payment is the present value of the notional amount + interest payment)
SUM = 1,031,820.66
- Calculate the 4 quarterly payments on the GB side
60 - (GB notional) * (GB fixed rate) * PVA = (8,333) * (.00235) * (.9752) = 19.0969
150 - (GB notional) * (GB fixed rate) * PVA = (8,333) * (.00235) * (.9700) = 18.9951
240 - (GB notional) * (GB fixed rate) * PVA = (8,333) * (.00235) * (.9680) = 18.9559
330 - [(GB notional) * (GB fixed rate) + (GB notional)] * PVA = [(8,333) * (.00235) + (8,333)] * (.9700) = 8,018.4792
(note that the last payment is the present value of the notional amount + interest payment)
SUM = 8,075.53
- Our answer needs to be in GB, so the Yen total (1,031,820.66) needs to be converted to GB.
1,031,820.66 / 125 = 8,254.57
- Net the values: 8,075.53 - 8,254.57 = -179.04
This was so helpful thanks so much! I’m gonna crack on now with a few more swaps questions, lets see how it goes!
Cheers