Implied Volatility as a Black-Scholes Market-Price Convention
Summary
The document clarifies that implied volatility conventionally means the volatility input to the Black-Scholes or Black formula that reproduces an observed option price. Parameters calibrated in another model, such as a stochastic variance model, are not generally called implied volatility. A different model can generate option prices that are then translated into Black-Scholes implied volatilities by inversion.
The discussion also distinguishes market-implied volatility from a trader’s own forecast of future volatility. Implied volatility is inferred from option prices, which reflect market conditions and trading motives; it is not itself a direct forecast. Using it as a pricing input requires model assumptions, including a distributional form and simplified dynamics. The example illustrates an interpretation of volatility as a one-standard-deviation move under a lognormal framing, but the note cautions that skew, excess kurtosis, and non-independent returns can limit that interpretation. Forecast volatility can instead be used as an input to estimate a model-based option value.
Key ideas
- Implied volatility conventionally refers to the Black-Scholes or Black input that matches a market option price.
- Parameters from a different pricing model are not generally called implied volatility.
- Prices generated by another model can be converted into Black-Scholes implied volatilities.
- Implied volatility is inferred from market prices and should not be confused with an independent volatility forecast.
- Its interpretation depends on modeling assumptions that may not match real return distributions or market dynamics.
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# What is implied volatility? # What is implied volatility? 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? ## Answer by Gordon (score 9, accepted) https://quant.stackexchange.com/a/28320 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. ## Answer by drobertson (score 6) https://quant.stackexchange.com/a/28443 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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