Toward a More Exact Option Pricing Relation
Binomial Model:
Suppose the current price of a stock is $110 and that
at the end of one period the stock will have either risen 10% to $121 or
fallen 10% to $99. Also suppose that the risk-free rate is 5% and that
we can buy a one-period call on the stock with an exercise price of $99.
Consider setting up the following portfolio:
|
t=0 |
t=1 |
||
|
S=$99 |
S=$121 |
||
| Buy Call |
-C |
0 |
$22 |
| Short Share |
$110 |
-$99 |
-$121 |
| lend $94.30 |
-$94.30 |
$99 |
$99 |
|
$15.70-C |
$0 |
$0 |
|
What does this imply about the value of C? Why?
Where does the above portfolio come from?
