How to value this swap question ?

CFA Level II Derivatives
#1

Guys. If somebody can please help with a detailed step by step answer to answer this below question please.

A currency swap has a remaining life of 15 months. It involves exchanging interest at 10% on 20 million pound sterling for interest at 6% on USD 30 million every year. The term structure of interest rates in both UK and US is currently flat and if the swap were negotiated today the interest rates exchanged would be 4% in USD and 7% in sterling. All interest rates are quoted with annual compounding. The current exchange rate is USD 1.85 per pound. What is the value of the swap to the party paying sterling? (Assume USD is domestic currency) (Assume continuous compounding)

Thanks a lot

#2

I get −£4,852,072.

Compute the PV of the USD payments, discounted at 4% per year, and compute the PV of the GBP payments, discounted at 7% per year. Divide PV(USD) by USD/GBP 1.85, then subtract from that PV(GBP).

#3

Thanks for your response. I actually have a solution with me, But i am unable to understand it, if you could just have a look and try to explain me this.

Similarly 1.7824 discounted @ 4% for 3 months, and 30.278 discounted at 4% for 15 monthsthis below 1.966 figure is discounted @7% for 3 months, and 20.215 figure discounted at 7% for 15 months

here is the screen shot of the ans - https://imgur.com/a/HCnqr

My doubt here is what are these 3 m and 15 m figures? and in case of sterling first, why are we discounting 2 million for 3 months at 7% and then discounted 22 m for 15 months, and similarly for usd

If in all we have 2 pay 2 million interest, why are we caluclation 2 million present value for 3 months and again 2+20=22 million present value for 15 months?

Thanks

#4

Hello S2000magician,

Would you be so kind as to detail the explanation?

I find -2,04 million.

#5

The general rule for valuing derivatives of any sort is:

Value = PV(what you will receive) – PV(what you will pay)

It’s an annual-pay swap with 15 months till expiration, so the last (ultimate) payment is 15 months from today and the next-to-last (penultimate) payment is 15 − 12 = 3 months from today. The discount rate for the USD payments is 4% per year and the discount rate for the GBP payments is 7% per year.

The present value of the USD payments is, therefore, USD1,800,000 / 1.043/12 + USD31,800,000 / 1.0415/12 = USD1,782,437 + USD30,278,576 = USD32,061,013.

The present value of the GBP payments is, therefore, GBP2,000,000 / 1.073/12 + GBP22,000,000 / 1.0715/12 = GBP1,966,455 + GBP20,215,894 = GBP22,182,350.

To determine the value to each party, we need either to convert USD to GBP (at the USD/GBP spot rate) or to convert GBP to USD (at the USD/GBP spot rate). As we’re valuing this for the sterling payer (the USD receiver), let’s convert GBP to USD: GBP22,182,350 × USD1.85/GBP1.0 = USD41,037,347.

Therefore, the value to the sterling payer is USD32,061,013 − USD41,037,347 = (USD8,976,334).

Note: I just noticed the parenthetical about continuous compounding; I was using annual compounding. The differences are slight:

  • The PV of the first USD payment, for example, will be USD1,800,000 / e0.04×3/12 = USD1,782,090
  • The value is (USD8,894,736)
#6

Thanks but there are 15 months remaining so don’t we have to discount back to today at 15/12?

#7

I got it! Thanks a lot! Sorry for the question!

#8

Good to hear.

My pleasure.