Options

What is the definition of an option…?

 There are two kinds of options, call options and put options:

  • Call options give the right to buy the underlying asset at a certain date (expiration date), or in a certain period, against a predetermined price (strike price)
  • Put options give the right to sell the underlying asset at a certain date, or in a certain period, against a predetermined price

Most stock options are American options.

American options give you the right to exercise the option at any point in time between the time of buying and expiration.

Most index options are European.

European options can only be exercised at the expiration date. In most cases European Options are subjected to a cash settlement procedure. 

What factors determine the value of an option

The value of an option can be divided into two parts:

  • Intrinsic Value
  • Expectation Value

The intrinsic value is the value of the option if you would exchange the option into the underlying asset at this moment. All the rest is called expectation value.

Most important Factors:

  • Value of underlying asset
  • Strike price
  • Time left till expiration
  • Volatility of the underlying asset
  • Intrest rate
  • Dividend of underlying asset

To calculate the value of American options mostly used are the binominal models. Black and Scholes is mostly used to calculate the value of European options.

In spite of all these variables there is no “true” value for an option. As they say, the market is always right. The best thing is to determine what kind of movement of the asset you expect, depending on that you can enter in an option construction. 

To see what sort of option strategies are possible take a look at the option strategies page. With any kind of option construction you have to keep in mind that the lesser time left to expiration the more leverage.

However the value of the option goes towards it's intrinsic value as we come closer to expiration. This means that everyday nothing happens the options value decreases. This is also known as the theta of an option.

Call-put parity

This term is frequently used among traders. A call can synthetically be created by buying the stock and the put option with the same strike price.

Call = Stock + Put

The easiest way to explain this is in a profit loss graph. First of all the profit/loss graph of the 100 call of stock X.

Second of all the  profit/loss graph of buying the stock at 100 and buying the 100 put. In the graph the profit and loss lines of both the stock and the 100 put are shown. Below the 100 level the losses on falling stock price are compensated by the profits of the put. Above 100 there is just the profit of the stock. Synthetically we reached the same results as the owners of the 100 call. This is also known as call-put parity. 

Of course using the same method we can also see that

put = -/- stock + call

Exercising options Normally options are exercised at the expiration date. However American option holders have the right to exercise prior to expiration.

The only event in which it can be useful to exercise a call option prior to expiration is the day before the ex-dividend date. If the following scenario is true,

theoretically you should exercise:  If (dividend) > ( interest over strike until expiration) + ( value of the put with the same strike as the call under evaluation)

The explanation for above formula is the following:

  • Benefit: In case you exchange the options for stock you receive a dividend. 
  • Loss: Suppose you have the 100 call and the stock value is 110. For the call option you need an investment of 10. After exercising you need an investment of 110. The extra investment you need when exercising a call is reflected in the second part of the formula.
  • Loss: Owners of the 100 call can only loose 10. Owners of the stock can loose 110. If owners of the stock buy the 100 put they have synthetically the same position of the call owner.  This is reflected in the third part of the formula. Only for very deep in the money puts it is sometimes better to exercise prior to expiration. However never exercise a put if you expect a dividend in the future.