Stock Options - some clarification needed

[SURAJM]

Hi David,

In John Hull i have seen the following three terms being used interchangibly to refer the same thing?

1) Price of an option
2) Payoff of an option
3) Premium paid on an option

This confusion especially came when i was reading the binomial trees chapter in Hull

Do they refer to the same thing?

Suraj

 

[David Harper CFA FRM]

Hi Suraj

In Hull, typically, option price = option premium = option value; i.e., the model price (given by an option pricing model, as in the B-S or binomial), which is often 20-50% of face value, that gives the price you would buy/sell the option. This option value/price = time value + intrinsic value. (though price can refer to stock price or strike price).

Payoff is the gain when the option is exercised (so, it will equal intrinsic value at exercise).

Profit = payoff - premium/price.

For example, if B-S or binomial says option is worth 15% of face today, and stock & strike price = $10, then

price/value/premium = $1.50
if exercised when stock goes up to $13, payoff = $13 stock - $10 strike = $3 payoff
profit = $3 payoff - $1.50 premium

David

Append: but please note the time dimension can, I suppose, introduce a difference between option premium and option value. You may pay the $1.50 premium to buy a call option. Then a few days elapses, due to time decay, all other things being equal, the (T+days) option value is < $1.50. So, we would tend to say the new option "price" or "value" is < $1.50.