# Delivery Price of a Forward Contract

• March 14th 2011, 01:25 PM
ft_fan
Delivery Price of a Forward Contract
Hi all,

I am beginning a new module on Monday which looks how Mathematics is used in the financial world. We have been asked to do some reading and answer the following question, which I am struggling to get my head around:

A trader wishes to sell US Dollars in 6 months time in exchange for Sterling. After considering his options, he chooses to sell a six-month forward contract on the \$/£ exchange rate. Show that the delivery price is given by $f_{0}=0.6601$\$/£.

I am having issues grasping the concept of selling a current asset for a price it may be worth in the future, and I cannot find an online resource that will talk me through it. Any pointers much appreciated.

• March 14th 2011, 06:39 PM
Volga
Generally, the difference between today's and future exchange rates can be explained by different interest-free rates paid in these two currencies. (So time has different money value in USD and GBP).
• March 23rd 2011, 06:13 PM
ft_fan
My apologies -we are also given the following information:
• Risk-free interest rate operating in the UK: 2.63%
• Risk-free interest rate operating in the US: 1.96%
• Spot exchange rate: \$1 = £0.65785
• Exchange rate volatility: 26% per annum
• March 23rd 2011, 07:03 PM
Volga
you might need to use the Black-Scholes model since you are given volatility. and if you don't know what it is, you'd better wait to see it in the lecture, as you are not supposed to be able to derive it yourself )))

outside B-S, I attach a simple spreadsheet that explains how xrates work, I got to 0.6600 (not 0.6601 as required) but I didn't use B-S for that

Attachment 21238
• March 23rd 2011, 11:52 PM
Volga
If I use e^{rt}, ie continously compounded interest, I get that final 0.0001 (ie 0.6601):

$F_t=F_0e^{(r-q)(T-t)}$ this is a general formula where r-q can be either risk free rate minus divident stream, or, in your case, it is different in risk-free rates in domestic and foreign currency
T=1 year, t=1/2 year

$F_t=0.65785e^{(2.63/100-1.96/100)(1/2)}=0.660057, or 0.6601$ rounded to the nearest 1/10,000

And I didn't have to use volatility for that.