A bond is priced at £95 per £100 nominal, has a coupon rate of 5% per annum paya

Question

A bond is priced at £95 per £100 nominal, has a coupon rate of 5% per annum payable half-yearly, and has an outstanding term of 5 years. An investor holds a short position in a forward contract on £1 million nominal of this bond, with a delivery price of £98 per £100 nominal and maturity in exactly 1 year, immediately following the coupon payment then due. The continuously compounded risk-free rates of interest for terms of 6 months and 1 year are 4.6% per annum and 5.2% per annum, respectively.

Calculate the value of this forward contract to the investor assuming no arbitrage.

Explanation / Answer

Formula: f = S- I – Ke-r(T-t)

Where,

t is the present time

T is the time of maturity of the forward contract

r is the continuously compounded risk-free rate of interest for the interval from t

to T

S is the spot price of the security at time t

I is the present value, at the risk-free interest rate, of the income generated by the

security during the interval from t to T

K is the delivery price of the forward contract

f is the value of a long position in the forward contract

Here, working with £100 nominal,

S = 95, K = 98, T t =1, r = 0.052

I = 2.5 (e -0.046 x 0.5 + e 0.052 x 1) = 4.81648

f = 95 - 4.81648 - 98e -0.052 = -2.85071

The value of the investor’s short position in a forward contract on £1 million will be:

(1,000,000 / 100) x – f
=> 10,000 x – (-2.85071)
=> 10,000 x 2.85071 = £28,507

So, the value of this contract to the investor assuming no arbitrage is £28,507.

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