Question

I am not sure how to construct a swap diagram regarding to information given on the question,
also, not sure how to explain the principal which underpins swap valuation

An interest rate swap with notional value of £10m has a remaining life of 9 months. The terms of the swap require the 6-month LIBOR to be exchanged for 6.1% per annum with semi-annual compounding. The current swap rate being exchanged for LIBOR in swaps of all maturities is 5.1% per annum with continuous compounding. Three months ago, the 6-month LIBOR was 5.2% per annum.

(a) Explain, using a diagram, how the swap is constructed.

(b) Calculate the value of the swap to the party paying the floating rate. Assume that the swap takes place without involving a financial intermediary.

(c) Explain the principal which underpins swap valuation.

Answer 1

Four months exchange notational principal (Received) is calculated below:

Available info:

Compounded Time period = 0.5

Six month LIBOR Exchange rate = 6.1%

9-months principal = £10 million

Calculate:

Three months principal (received) = Compounded Time period * Six month LIBOR Exchange rate * 9 months principal

Three months principal (received) = 0.5 * 0.061 * £10 million

Three months principal (received) = £0.305 million

Three months exchange notational principal (Paid) is calculated below:

Available info:

Compounded Time period = 0.5

Six month LIBOR Exchange rate = 5.2%

9 months principal = £10 million

Calculate:

Three months principal (Paid) = Compounded Time period * Six month LIBOR Exchange rate * 9 months principal

Three months principal (Paid) = 0.5 * 0.052 * £10 million

Three months principal (Paid) = £0.26 million

Fixed rate bond = 0.305e−0.051 × 3/12 + (10 + 0.305)e−0.051 × 9/12

Fixed rate bond = 0.301 + 9.918

Fixed rate bond = £10.219 million

The value of the floating-rate bond underlying the swap is

(10 + 0.26)e−0.051 × 4/12 = £10.087

Floating rate bond = £10.087 million

a.

Value of the swap to the party paying floating = Fixed rate bond - Floating rate bond

Value of the swap to the party paying floating = £10.219 million - £10.087 million

Value of the swap to the party paying floating = £0.132 million

b.

Value of the swap to the party paying fixed = Floating rate bond - Fixed rate bond

Value of the swap to the party paying fixed = £10.087 million - £10.219 million

Value of the swap to the party paying fixed = -£0.132 million