A financial option also known as call option is a contract that gives to his buyer the right, but not obligation, to buy or sell goods or values (the underlying assets, that can be actions, stock exchange indexes, etc.) at a predetermined price (strike or price of exercise), up to a concrete date (expiration).
Around 600 B.C. there was a guy in olg Greece named Thales. Like many others, Thales liked to think about the stuff he saw every day. Olives were a big commodity back in those times; so, for several seasons around that time he wondered why the olives weren’t blossoming, which was sending many citizens and farmers into distress.
Like many other of his contemporaries, He was more of a mathematician than a philosopher, so he studied how olives went from the trees to olive presses and tried to predict when the harvest would come once again.
he was confident that the olives would grow abundantly in the coming year. An astute businessman for his time, Thales cut a deal with many of the farmers, buying the “right” to use their olive presses within a given period of time in exchange for a nominal fee. The farmers, skeptical that the olives would never come again, largely accepted his offer because they figured that getting some profit, no matter how small, was better than getting nothing at all…
Legend says that he never exercised these options and let the farmers slide, partly because he had no time to get involved in the olive business. In any case, this is believed to be one of the very first options trade on record.
The models of evaluation of options were very simple and incomplete until 1973, when Fischer Black, Myron Scholes and Robert C. Merton published the model of evaluation of Black-Scholes-Merton. In 1997 Scholes and Merton got the Nobel Prize of Economy for this work. Sadly, Fischer Black died in 1995 reason by which it was not rewarded but undoubtedly he had been one of the prizewinners.
The model of Black-Scholes-Merton gives a few theoretical values for the Europeans options put and call on actions who do not pay dividends. The key argument is that the investors could, without covering any risk, compensating long positions with short positions of the action and continuously fitting the ratio of coverage (the value delta) if it was necessary. Assuming that the price of the underlying one continues a chance walk, and using stochastic methods of calculation, the price of the option can be calculated where there are no possibilities of arbitration. This price depends only on five factors: the current price of the underlying one, the price of exercise, the type of interest frees of risk, the time up to the date of exercise and the volatile nature of the underlying one. Finally, the model also was adapted to be capable of valuing options on actions that pay dividends.
The availability of a good estimation of the theoretical value contributed to the explosion of the commerce of options. There have developed other models of evaluation of options for other markets and situations using arguments, assumptions and hardware seemed, as the model of Black for options on futures, the method of Monte Carlo or the model binomial.