St stands for the stock price at time t and K stands for the strike of the option.
Argument on p. 158 of Hull (1993).
The following argument is based on pp. 160/161 of Hull (1993).
Vega is not actually a Greek letter, but in option theory it is still referred to as an option Greek.
Because the Black-Scholes formula contains the Normal distribution, this particular equation in the unknown σ cannot be solved analytically. However, there are methods, like the Newton-Raphson method, to solve it to any required accuracy. An example of such a method will be treated shortly.
This example is almost identical to the example on p. 229 of Hull (1993), only the numbers are different.
This is not totally correct because if the stock price changes, δ also changes. So, in fact, it should be that if the stock price changes by a small amount the option price changes by 50% of that amount. But, for the sake of this example it is expressed in a $1 stock price movement.
The intrinsic value of an option is the payoff of that option were it exercised immediately. See Section 1.3.
The value of a European call option on a dividend paying stock can be less than intrinsic, which will be shown in Section 5.3.
Argument put forward on p. 158 of Hull (1993).
One could think that the European put option case differs slightly, since the price of this option is not necessarily as much as the intrinsic value. But, by noting that in this case the option part ...