I am currently reading the famous article by Fischer Black and Myron Scholes called 'The pricing of Options and Corporate liabilities'.
Just at the beginning of the article, they go on and explain what an option is on the example of a 'call' option. This means, the option one takes is the right to buy a stock at 'strike price' on expiration date. Thus, to earn something, the strike-price must be lower than the stock price at maturity to make money. What puzzles me is the following sentence :
In general, it seems clear that the higher the price of the stock, the greater the value of the option. When the stock price is much greater than the exercise price, the option is almost sure to be exercised. [...] On the other hand, if the price of the stock is much less than the exercise price, the option i sure to expire without being exercised, so its value will be near zero.
If the expiration date is very far in the future, then the price of a bond that pays the exercise price on the maturiy date will be very low, and the value of the option will be approximately equal to the price of the stock. On the other hand, if the expiration date is very near, the alue of the option will be approximately equal to the stock price minus the exercise price, or zero, if the stock price is less than the exercise price. Normally, the value of an option declines as its maturity date approaches, if the value of the stock does not change.
Could someone explain to me the part in bold : in particular 'the price of the a bond that pays..' and why the value of the option should decline in time.