Forex Talking

It should be obvious by now that the value of the volatility parameter is crucial to the long volatility player. If one believes that future volatility is going to be 15% then with the stock price at $99, the break-even option price is $5.46. To make a profit one would really only get involved at a lower price or hope that future volatility will be higher than 15%. In the jargon of the market we say that the price of $5.46 is implying a future volatility of 15% or that 15% is the implied volatility of the option. By buying the option at $5.46 one is in essence paying up front for all the future rehedging profits associated with a stock price volatility of 15%. We say that we are buying volatility at 15%.

Consider now another situation. Another stock is priced at $109 that also has a one-year call option with an exercise price of $100. The option is offered at a price of $10.12. Examination shows that this price implies a volatility of only 10%. This option only requires a future stock price volatility of 10% to break even. If the two stocks in question are likely to exhibit similar volatility we can say that the option at $10.12 is cheaper than the one mentioned above priced at $5.46 The new option, although more expensive in dollar terms, is cheaper in volatility terms than the original one. So the implied volatility can be used as a measure of relative value. Options with different times to maturity, different stock prices and different exercise prices can be compared by simple reference to the implied volatility.

How does one calculate the implied volatility? As with most calculations involving options no one ever really has to go to the bother of deriving implied volatilities since most information services provide on-line live values.

However, the process is relatively straightforward. As mentioned above, the first four inputs into the model are known: the only unknown is the volatility. What is known, of course, is the market price of the option. In order to find the implied volatility one proceeds as follows. Substitute all the four known values into the model. Try substituting any volatility value, say25%, and calculate the model price. Ask the question: is the model value the same as the market value? If the answer is yes then the implied volatility of the option is 25%. If the answer is no then try another value, say 24 or 26%, and repeat the procedure. Eventually one will arrive at a volatility that will give a model price that exactly matches the market price.

As an example let this be 12%. This then is the implied volatility of the option. We say that the market price of the option is implying (if the model is valid) that the future volatility is going to be 12%. This procedure of trying various input values to match output prices may seem cumbersome and crude but in reality this is not so. There are well-known mathematical techniques that produce rapid and accurate results.