When a trader enters a volatility into a theoretical pricing model, what exactly is he feeding into the model? We know the mathematical definition of volatility—one standard deviation, in percent terms, over a one-year period. Beyond this, we still have the question of interpretation. Does the number represent a realized volatility or an implied volatility? Are we talking about historical volatility or future volatility? Long term or short term? The volatility a trader chooses may vary depending on the answers to these questions.
Consider this situation:
Underlying price = 100.00
Time to expiration = 8 weeks
Interest rate = 0
Implied volatility = 20 percent ...