- A key challenge in using either Black-Scholes-Merton or a binomial option pricing model is accurately estimating the stock’s return volatility.
- Two common approaches for estimating volatility:
**Historical Approach:**This assumes that past volatility is representative of future volatility.- For BSM, the annualized standard deviation of price returns is applied.
- σ
_{annual}= σ_{periodic}* √periods per year - 250 trading days per year is a convention when the periodic standard deviation is daily; 12 is applied for monthly data; 52 is applied for weekly data.
**Implied Volatility Approach:**This takes the current market price of the option and back solves for the implied value of volatility via the option pricing model.- The output of the implied volatility approach is an estimate for volatility that equates the BSM price of the option to the market price of the option.
- Analysts and traders can use this approach to form opinions as to whether an option price is too high or too low based on their own expectations for volatility relative to the implied volatility priced into the option.

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