Whats the worth of an option?

There are 4 main things that influence the price of an option.

First, the intrinsic value. This is the difference between the underlying value (eg. stock price) and strike price. Formula = Underlying price – Strike price.

However the intrinsic value cant be negative (as the share price cant be negative). Therefore only the money option has an intrinsic value.

Eg. Stock price = 20 Euro, Strike price = 15 Euro

Intrinsic Value = 20 Euro – 15 Euro = 5 Euro -> In the money

If the option is out of the money or at the money it has an intrinsic value of 0

Second, the time value of the option – which decreases with time. Therefore all options have a time value till the expiration date.

The longer the expiration date lies in the future, the more interest effects one could achieve. For that reason, it is important to calculate the present value as the exercise price doesn’t reflect the option value enough.

Third, the volatiliy of the underlying stock

Fourth, the Interest Rate

For a call with a fixed expiration date (european) the minumum value can be calculated like this:

Call min Price = Spot price (of underlying ) – Excercise price (of option) / (1+ interrest rate) ^ time till maturity

Formula: C(all) = S – [Ex/(1+r)^T]

Example:

S = 100
Ex = 50
T = 2 year
r = 5

100 – 50 / (1+0,05)^2 =

The call must have a minimum price of xx. Otherwise, you could find arbitrage opportunities.

For a put with a fixed expiration date (European) the minimum value can be calculated like this:

Put min price = Excercise price of option/ (1+ interest rate)^ time till maturity – Spot price (of underlying)

Formula: P(ut) = [Ex/(1+r)^T] – S

On the expiration date the value of a call is:

C= S (spot price) – Ex (strike price)

On the expiration date the value of a put is:

P = Ex (strike price) – S (spot price)