Options

Option is a derivative financial instrument. This means, not only the option itself, also something under it, is a part of the contract. This something, we call it underlying instrument, can be for example stock, bond, swap, amount in foreign currency, stock or bond index, gold, copper, cattle meat or even a nice weather.

There are two kinds of options: call and put. Exact definition is:

The buyer of a call option buys a right (but no obligation) to buy later the underlying instrument (from the seller of the option) for a fixed price (the strike of the option).
The buyer of a put option buys a right (but no obligation) to sell later the underlying instrument (to the seller of the option) for a fixed price (the strike of the option).

For this right, the buyer of the option has to pay to the seller premium in advance: the price of the option. When the buyer of the option exercises his right, we speak about exercise of the option. By exercise one can agree either upon physical delivery or cash settlement. Physical delivery and e.g. call option means, the buyer of the option pays the strike and get the underlying instrument. Cash settlement means, the seller of the option has to pay to the buyer the price difference between price of the underlying and strike. Options do not last forever, (otherwise they were too expensive). They have a maturity. If they are not exercised until maturity, they expire worthless.

Option price

In order to determine a price or a value of the option, we need at least the following specifications:

The longer the maturity, the greater the fluctuation of an underlying price. We assume that the fluctuation grows with the square root of time. The standard deviation of an underlying price for the time of exactly one year we call the volatility of the underlying price. The standard deviation of the underlying price is then , where σ is the volatility and t is the time to maturity in years.

Sensitivities of the Option Price (Greeks)

Not only the price of the option is interesting but also how the price changes if we change some of price building components. The most important sensitivity is Delta: the partial derivative of an option to the price of an underlying. Delta=0.5 means, if the price of an underlying changes to a (very small) amount, the price of the option changes only to a half of this amount. Other sensitivities are:

Classification of Options

We can classify options on the underlying type, on kind of exercise and on exercise amount. By classification on the underlying type we can distinguish between:

By classification on kind of exercise we have:

By exercise amount we can divide between: