Does the price of a European option always increase as the maturity date increases?

Answer 1

First, the price of a European-style option does not always increase as the maturity date increases. Deep in the money European-style puts for an index with realtively low volatility will decrease in price as the maturity date increases. For example, the December 2009 SPX put with a strike of $1,900 is rounghly $377 while the December 2008 SPX put with a strike of $1,900 is roughly $415.

Excluding deep in the money puts, longer maturity dates are more valuable because they allow more time for the price of the underlying to change, and the longer it has to change the more likely it is that the size of the change will be bigger.

Answer 2

Remember, there are two sources of value to an option. You have the intrinsic value - how far in the money it is...or zero since it is an option. You also have time value - the value of being able to wait and hope that the volatility works in your favor. As you approach maturity, you would assume that the price would converge on the intrinsic value.

One way to look at this is an option that has an intrinsic value of $1 and is 1 minute away from maturity would probably only be worth around $1 (very little time value remaining). However a 90 day option with an intrinsic value of $1 must be worth more than $1 due to the time value.

Answer 3

European or American option the price need not increase as the expiry date advance. In fact for same strike price the option value decreases if it is out of the money.
If in the money then the 45 degree line come into play where the option value increases in direct correlation to the stock price increase. This of course is the Intrinsic value. Option value is not intrinsic value alone. It has 'time value' as well.
So before expiry out of money the intrinsic value and time value move together. Before expiry the time value declines and the intrinsic value advances. So you get the value slightly higher depicted above the 45 degree line.