- Introduction: A Simple Market Model 13
- Cash $55 from the risk-free investment.
- Buy the asset forFdollars, closing the long forward position, and return
the asset to the owner.
Your arbitrage profit will beV(1) = 55−F>0, which once again violates
the No-Arbitrage Principle. It follows that the forward price must beF=55
dollars.
Exercise 1.5
LetA(0) = 100,A(1) = 112 andS(0) = 34 dollars. Is it possible to
find an arbitrage opportunity if the forward price of stock isF=38. 60
dollars with delivery date 1?Exercise 1.6
Suppose thatA(0) = 100 andA(1) = 105 dollars, the present price of
pound sterling isS(0) = 1.6 dollars, and the forward price isF=1. 50
dollars to a pound with delivery date 1. How much should a sterling
bond cost today if it promises to pay£100 at time 1?Hint:The for-
ward contract is based on an asset involving negative carrying costs (the
interest earned by investing in sterling bonds).1.6 Call and Put Options
LetA(0) = 100,A(1) = 110,S(0) = 100 dollars and
S(1) =
{
120 with probabilityp,
80 with probability 1−p,where 0<p<1.
Acall optionwithstrike priceorexercise price$100 andexercise time1is
a contract giving the holder the right (but no obligation) to purchase a share
of stock for $100 at time 1.
If the stock price falls below the strike price, the option will be worthless.
There would be little point in buying a share for $100 if its market price is
$80, and no-one would want to exercise the right. Otherwise, if the share price
rises to $120, which is above the strike price, the option will bring a profit of
$20 to the holder, who is entitled to buy a share for $100 at time 1 and may
sell it immediately at the market price of $120. This is known asexercising
the option. The option may just as well be exercised simply by collecting the