You have probably heard the term “Implied Volatility” tossed around a lot when it comes to option trading. If you did not know what it means, this post is for you.
The landmark Black and Scholes equation, developed in the 70’s, gives a “fair” price of an option. You just plug in the interest rate, time to expiry, the strike price and volatility and you are set, the formula would give you the price you should pay for an option. There is a slight problem though. While interest rate, time to expiry and strike price are all observable from the market, the volatility is not.
One of the biggest drawbacks in the Black and Scholes model, is the assumption of constant volatility. The Black and Scholes model assumes that the future volatility of the stock is constant and does not change until expiry. So not only we need to assume we know what the future volatility would be, we need to assume it is constant throughout the period! Of course, this assumption was not made just because the Black and Scholes felt like it mind you. So before you get into the drawing board, know there were some technicalities involved to make sure the end result would be a managable formula.
So where does implied volatility enter the picture? If you want to buy an option on a stock , there is a price on the market. Suppose it is 20$. The implied volatility is the volatility that you need to plugin to the Black and Scholes formula to get the price the market offers. In our case 20$. Hence the name, it is implied by the market.
The curious bunch of you would have to wonder at this point, is the implied volatility on average equals the real volatility (in retrospect)? Remember that the volatility in the Black and Scholes formula assumes it is the future volatility. So looking back, we can ask the question whether the traders in the market were right on average in their assumptions of the future volatility. The question is interesting as it turns out that the answer is no. Does it mean that the market misprices options or does it mean the Black and Scholes formula is not a “fair” price?
In the next posts I’ll expand on the topic and explain some recent theories that touch upon those issues.
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