# Implied or historical volatility to calculate theoretical options price with black scholes?

According to the black scholes model, volatility is one of the variables to calculate the fair price of an option. However, it doesn't specify which volatility should I use. Should I take the annualized standard deviation or should I use the implied volatility?

## 1 Answer

Option pricing models used by exchanges to calculate settlement prices (premiums) use a volatility measure usually describes as the current actual volatility. This is a historic volatility measure based on standard deviation across a given time period - usually 30 to 90 days.

During a trading session, an investor can use the readily available information for a given option to infer the "implied volatility". Presumably you know the option pricing model (Black-Scholes). It is easy to calculate the other variables used in the pricing model - the time value, the strike price, the spot price, the "risk free" interest rate, and anything else I may have forgotten right now. Plug all of these into the model and solve for volatility. This give the "implied volatility", so named because it has been inferred from the current price (bid or offer).

Of course, there is no guarantee that the calculated (implied) volatility will match the volatility used by the exchange in their calculation of fair price at settlement on the day (or on the previous day's settlement). Comparing the implied volatility from the previous day's settlement price to the implied volatility of the current price (bid or offer) may give you some measure of the fairness of the quoted price (if there is no perceived change in future volatility). What such a comparison will do is to give you a measure of the degree to which the current market's perception of future volatility has changed over the course of the trading day.

So, specific to your question, you do not want to use an annualised measure. The best you can do is compare the implied volatility in the current price to the implied volatility of the previous day's settlement price while at the same time making a subjective judgement about how you see volatility changing in the future and how this has been reflected in the current price.