Consider a European call option on a stock. 1. Show that the expression for the Greek at time is...

Consider a European call option on a stock.

1. Show that the expression for the Greek at time is
indeed given by . You can take the derivative using the expression ( 14.17 )
with or directly ( 14.18 ) and simplify the expressions. Note that

2. Since is always positive, this shows that the higher
the stock price, the higher is the option price.

3. Determine the value of at time 0 for the example of
the stock used in this section.