By Frans de Weert
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Extra info for An introduction to options trading
However, it is possible to estimate the interest rate so accurately that this variable can effectively be treated as known. With this knowledge it is easy to explain the concept of implied volatility. The price of an option comes about from supply and demand. This is of course confusing. The Black–Scholes formula gives the price of an option, which would suggest there could only be one price for an option, regardless of supply and demand. But, as has been pointed out, at the time an investor has to decide whether or not to buy an option, he does not know what the volatility of the option will be during the term of this option.
This is a logical name because, in calculating it, the market price of an option is used. Which means that the calculated volatility is implied by the market and, therefore, it tells what the market thinks the volatility of the underlying stock will be during the term of the option. In conclusion, the implied volatility is nothing more than that volatility, such that when it is substituted into the Black–Scholes formula the output is equal to the market price of the option. The idea of implied volatility is illustrated by the following example, which is based on the example on p.
An alternative strategy2 is to keep the option and short the underlying stock. This guarantees a payoff of at least $10. On top of that, interest is earned over $50, since this was received by shorting the stock, which is more than the interest earned on the $10 were the American option exercised immediately. This means that the discounted expected payoff is more than $10. However, for an American put option it can be profitable to exercise the option early. 3 Consider an investor with a put option on Royal Dutch/Shell with a strike price of $40 and an expiration date in 1 year.