Question

What two-sided prices can be constructed for the GBP/USD 3- month outright, given the following? The 6-month period is 183 days. (You may assume a year is 360 days) GBP/USD spot: 1.4120/26 GBP 6-month interest rate: 5.10/5.20% USD 6-month interest rate: 4.30/4.40

Answer 1

To find this two sided price we need to use a process for bid and offer rate separately.

First rate:

Let us assume that we need to pay $ 1 after 3 months( i.e. 91 days) for this we will invest the PV if this $ 1 now in US market @4.30% p.a. 3 month rate is 4.30%*91/360 =1.01086%

So the PV is = 1/(1.010869) = $.989248

To invest this amount we need to buy $ for pound at spot offer rate i.e. 1.4126 GBP per USD

So we need 1.4126× .989248 = 1.39741 pound

We have to borrow this at 5.20% from UK market

This our borrowing will mature at 1.39741× (1+.0520×91/360)=1.4158 GBP per USD, now this rate is 3month offer rate.

Second rate:

Now let us assume that we will receive $ 1 after 3 months

So we will borrow the PV of this amount at 4.4% from $ market

I.e. the amount we get now = PV IS = 1/(1+.044×91/360) = .989$

We need to sell this for pounds at spot bid rate i.e. .989×1.4120=1.39647£

Now we will invest these £ in £ market at 5.10%

So after 3 months we will get £1.3964×(1+.0510×91/360) = 1.4144 GBP per USD this is our bid rate at which we will be able to sell our USD after 3 months.

Our quotation is GBP per USD = 1.4144/1.4158

Or it can be written as 1.4144/58