I always understood implied volatility as a volatility I need to plug into BS in order to get the market price.

My question is if I am using different model, does it mean that implied volatility is the volatility I need to plug into pricing equation of the new model in order to get market price or am I still referring to BS?


In practice, an implied volatility always refers to the volatility that you need to plug into the Black-Scholes', or Black's, pricing formula to obtain the market price. You may have a different model (e.g., a Heston style stochastic variance model), for which you are able to calibrate the parameters by matching your model price to the market price. However, none of those parameters are called the implied volatility in general.

Sometimes, you can also specify some parameters for a model (e.g., the Heston model), and generate some vanilla option prices. Then, you can also calibrate Black's implied volatilites by matching the BS prices to your model prices.

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    $\begingroup$ Agreed. Implied volatility is the one model parameter for the Black/BS model, and often called that for the Normal/Bachelier model too. Other models have more than one model parameter, and none of them is usually called the implied volatility, though some of them may be "volatilities" in some loose sense. $\endgroup$ – experquisite Jul 27 '16 at 18:49

Ok, there is a basic misconception about Implied Volatility. IV is derived from the price of the options in the market. Not the other way around. We do use different IVs to estimate option prices in other conditions, but that is just bringing the equations full circle. The Black-Scholes and many other options models allow us to calculate the risk neutral (less cost of carry) Volatility that is Implied by the current price.

For example, a $7.85 price of a GOOGL call option with a 797.50 strike that is roughly at the money Implies that the stock has a Volatility of roughly 14.5%. Meaning that at a point 1 year from now a 1 standard deviation range would roughly be between 14.5% higher and 14.5% lower than the current price of GOOGL. Given stable conditions, GOOGL would have a price between those points 68.2% of the time.

This also assumes that the prices have a log-normal distribution, little to no excess kurtosis, no appreciable skew, are i.i.d. (not true) and many other factors.

The Black-Scholes and other formulas can also take IV and several other factors and calculate a price for the option. This is a handy tool to use when you would like to know the price of an option would be relative to changes in the price of the underlying, time, IV changes, interest rate changes, etc..

The real difficulty comes from the fact that the IV you are working with is just an extrapolation of market prices. This includes the distortions created from the profit motives of traders, incomplete information, portions of the options market not being motivated by profit (options as insurance ie. long/short funds).

If you want to know the value of an option you need to have a clear idea of what you believe the forecast volatility of the stock is. Once you have a way to determine the forecast volatility that makes sense to you that number can be used as the IV input to Black-Scholes or other equation. From that you can get the value of the option based on your belief of what will happen in the market.


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