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Its 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 stock prices are impossible Therefore it implies that if the share price was zero the put would have reached its highest
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