- Financial Engineering 205
As a result, VaR∼= 431 ,818 dollars. The final balance as a function of the
exchange ratedisb(d) = 80%×(8 , 000 , 000
d− 3 , 000 ,000)− 1 , 250 , 000
=
6 , 400 , 000
d− 3 , 650 , 000.
The break even exchange rate, which solvesb(d) = 0, is approximately equal
to 1.7534 dollars to a pound. In an optimistic scenario in which the pound
weakens, for example, down to 1.5 dollars, the final balance will be about
£ 616 ,666.
The question is how to manage this risk exposure.2.Forward Contract.The easiest solution would be to fix the exchange
rate in advance by entering into a long forward contract. The forward rate
is 1. 6 ×e−3%∼= 1 .5527 dollars to a pound. As a result, the company can
obtain the following statement with guaranteed surplus, but no possibility
of further gains should the exchange rate become more favourable:sales 5 , 152 , 315
cost of sales − 3 , 000 , 000
earnings before tax 2 , 152 , 315
tax − 430 , 463
net income 1 , 721 , 852
dividend − 1 , 250 , 000
result 471 , 8523.Full Hedge with Options.Options can be used to ensure that the rate
of exchange is capped at a certain level, whilst the benefits associated with
favourable exchange rate movements are retained. However, this may be
costly because of the premium paid for options.
The company can buy call options on the exchange rate. A European
call to buy one pound with strike price 1.6 dollars to a pound will cost
£ 0 .0669.^2 Suppose that the company buys 5 million of such options, paying
a£ 334 ,510 premium, which they have to borrow at 16%. The interest is
tax deductible, making the loan less costly. Nevertheless, the final result is(^2) For options on currencies the Black–Scholes formula has to be modified by replacing
the risk-free interest raterby the difference between the risk-free rates for the
currencies, in our case:−3%.