Actual, historical, implied...and definitions.P

I'd also add the underlying volatility, sampling (discrete) volatility, and external risk volatility (e.g., crash)...

Terminal Volatility?

Annualized standard deviation of returns. If only it were that simple!...Actual volatility is a measure of the amount of randomness in a financial quantity at any point in time. It's what Desmond Fitzgerald call the 'bouncy, bouncy'!! It's difficult to measure, and even harder to forecast but it's one of the main inputs into option pricing models!It's difficult to measure since it's defined mathematically via standard deviations which requires historical data to calculate...yet actual volatility is not a historical quantity but and instantaneous one.Realized/historical volatilites are associated with a period of time, actually two periods of time. We might say that the daily volatility over the last sixty days has been 27%. This means that we take the last sixty days' worth of daily asset prices and calculate the volatility. Let me stress that this has two associated timescales, whereas actual volatility has none! This tends to be the default estimate of future volatility inthe absence of any more sophisticated model. Eg we might assume that the volatility of the next sixty days is the same as over the previous sixty days. This will give us an idea of what a sixty-day option might be worth.Implied volatility is the number you have to put into the Black-Scholes option-pricing equation to get the theoretical price to match the market price. Often said to be the market's estimate of volatility.P

------Implied volatility is the number you have to put into the Black-Scholes option-pricing equation to get the theoretical price to match the market price. Often said to be the market's estimate of volatility.------Is Implied Volatility an unbiased estimator of the underlying's future Realised volatility?Yes or No?Why (Rational Expectations?)?How(Time window/Option's Maturity?)?When/Where (Type and/or market of underlying?)?Anthis

-----Is Implied Volatility an unbiased estimator of the underlying's future Realised volatility?-----Personally, I think the concept of biased/unbiased is far too subtle here! The market falls, people panic, they buy puts, the price of puts and hence implied volatility goes up. End of story. Where the price stops depends on supply and demand, not on anyone's estimate of future volatility (within reason).P

>> Realized/historical volatilites are associated with a period of time [...]>> Implied volatility is the number you have to put into the Black-Scholes option-pricing equation to get the theoretical price to match the market price. exactly.I heard (not sure who said it first) implied volatility is the wrong volatility that we plug in the wrong model in order to get the right (market) priceso the realized expected underlying volatility does not correspond to any implied volatilitybecause it has nothing to do with (the wrong) Black-Scholes !it is an intrinsic model-free concept related at best to the famous Portfolio of all strikes (cf. Carr & Madan or Derman)

Paul your story is right, at the end of the day, things come to demand and supply forces and moreover in derivatives unlike underlying markets there is no fixed (potential) supplied quantity. But you describe a case (an extremme event period) which might be considered as rather a statistical outlier. Furthermore, some practicioners (e.g. Riskmetrics guys) take this as given. I would be interested to listen opinions of forum members on this

Implied volatility levels the playing field so you can compare and contrast option prices across stikes and expirations.P

PaulAs I recall, the Implied volatility is related to the BS_Vol and Jump_Vol as follows:Imp_Vol (T,s) = BS_Vol (T) + Jump_Vol/N((s-1)/BS_Vol(T));where N(.) as ususal is the normal CDF, and s is the fraction of strike price.-newton

Forward volatility is an implied volatility or actual volatility at some date in the future. ForwardVol=sqrt[vb^2*b-va^2*a/(b-a)]Where time a and time b are dates in the future where a < b (e.g. a =1y, b = 2y). Thus, vb is the implied or actual volatility at time b and va is the implied or actual volatility at time a. Immediate forward volatility refers to a future date where a = b

>> ForwardVol=sqrt[vb^2*b-va^2*a/(b-a)]true if we have a dtereministic vol.otherwise it will more complicated ... we would need a model (local vol, stochastic vol)

I'd say that volatilities from multiple dimensions probably don't add as volatilities do in the one-dimension case. In fact, they don't add at all. Only the price components add. So you need to turn volatilities into implied volatilities before you add.-newton

Wednesday January 08, 2003 07:34 PM (NEW!) Reza wrote>> ForwardVol=sqrt[vb^2*b-va^2*a/(b-a)] > true if we have a dtereministic vol.> otherwise it will more complicated ... we would need a model (local vol, stochastic vol) Allright, I understand where you are coming from. But if we use the implied volatilities of var/volswaps with different maturities this kind of forumla should hold, by arbitrage?Z

Ziggy, I agree with you. The smile is really a second order effect in your case.