It's a very useful essay for those who are specialising in finance -

Explain why it has proved impossible to derive an analytical formula for valuing

American Puts, and outline the main techniques that are used to produce

approximate valuations for such securities

Investing in stock options is a way used by investors to hedge against risk. It is

simply because all the investors could lose if the option is not exercised before the

expiration rate is just the option price (that is the premium) that he or she has paid

earlier. Call options give the investor the right to buy the underlying stock at the

exercise price, X; while the put options give the investor the right to sell the

underlying security at X. However only America options can be exercised at any time

during the life of the option if the holder sees fit while European options can only be

exercised at the expiration rate, and this is the reason why American put options are

normally valued higher than European options.

Nonetheless it has been proved by

academics that it is impossible to derive an analytical formula for valuing American

put options and the reason why will be discussed in this paper as well as some main

suggested techniques that are used to value them.

According to Hull, exercising an American put option on a non-dividend-paying stock

early if it is sufficiently deeply in the money can be an optimal practice. For example,

suppose that the strike price of an American option is $20 and the stock price is

virtually zero. By exercising early at this point of time, an investor makes an

immediate gain of $20. On the contrary, if the investor waits, he might not be able to

get as much as $20 gain since negative...