Finance: Implied and Historical Volatility

[fairholme_wannabe]

For anyone with interest in capital markets and finance:

I am presently researching volatility (historical volatility and implied volatility), and the distributions of each have me completely baffled. First, let me preface this by saying that implied volatility is proxied via the ^VXO instead of the ^VIX, as it has more history.

That said, the mean of the ^VXO is 8 points higher (or approximately 62% higher) than the mean historical volatility across the life of my study (20+ years). Additionally, the distribution patterns are pretty dissimilar, as historical volatility is distributed with both much greater skewness and kurtosis than the ^VXO. WTF!? Any explications for why this is observed?

 

[gnatty8]

One is forward looking and risk neutral, the other is backward looking and realized, so risk does not play a part. Implied volatility is rarely if ever equal to historic probabilities. Why would I write an option for you with the expectation of only breaking even?

 

[JoelF]

What Gnatty said. My shorthand, non-quant explanation - implied vol is really just a way of quoting option prices, with option premium calculated using Black Scholes or some variant depending on the structure. Historic vol is the statistical volatility (maybe weighted) of a market data series. The option models are typically pretty bad approximations, so the market uses an implied vol surface which means the quoted vols vary by option strike and expiration. If you had a perfect option model and knew the exact values of all other parameters (e.g. risk free rate) then I guess implied vol would be constant across the surface and also equal to historic vol.

 

[fairholme_wannabe]

Originally Posted by gnatty8

One is forward looking and risk neutral, the other is backward looking and realized, so risk does not play a part. Implied volatility is rarely if ever equal to historic probabilities. Why would I write an option for you with the expectation of only breaking even?

Gnatty,

Thanks for your response. I'm not trying to say that implied volatility should be equal to historical volatility, per se. I'm more interested in their respective distributions. Does that explain why the distributions themselves are so dissimilar?

On the flip side, why would I buy an option from you with the expectation of losing money?

 

[gnatty8]

Originally Posted by fairholme_wannabe

On the flip side, why would I buy an option from you with the expectation of losing money?

Unless you are a market-maker, you have no choice. Have you heard of the bid-offer spread? You also might think your model is better, or your own forecast of vols are different than mine.

 

[Lostinthesupermarket]

On a related point is it true that implied volatility over the past 6 months or so has been a lot lower than realised ?

 

[fairholme_wannabe]

Originally Posted by Lostinthesupermarket

On a related point is it true that implied volatility over the past 6 months or so has been a lot lower than realised ?
Lost, with regards to 30 Day realized volatility v. implied volatility of S&P 100, between Oct. 20, 2008 and Jan. 6, 2009, there were 47 trading days where previous 30 day realized volatility was higher than implied volatility. Since then, however, implied volatility has been higher than realized every trading day.

 

[gnatty8]

Originally Posted by Lostinthesupermarket

On a related point is it true that implied volatility over the past 6 months or so has been a lot lower than realised ?

Would not be surprised.. One of the reasons for the existence of the volatility smile in implied vols.. Fat tails in asset returns.. Also not surprised that market makers may now be over-compensating..

 

[andrewhay]

I prefer to do analysis on volatility therefor I have taken implied volatility data from a company although It will be harder to to analyze without any expert experience but I love to do such kind of an analysis It's hard to crack the implied volatility but hope it can be effectively bypassed.