Trading Cheap or Expensive of Implied Volatility

[Liming]

Dear David,

I am confused after studying your spreadsheet (http://www.bionicturtle.com/premium/spreadsheet/4.b.8_implied_volatility/). I would appreciate it if you could kindly elaborate on how to determine whether a volatility or implied volatility is trading cheap or expensive?
What confused me specially is that I think given a market price, there could be only one implied volatility and this is obtained from the reverse engineering of BS pricing model. Whereas when we do pricing with BS pricing model, the volatility is one key variable that can take many possible input. I'm not sure how this single one implied volatility can be compared to the almost infinite collection of possible volatility inputs in order for us to figure out if it is higher or lower (trading cheaper or expensive respectively). What I mean is that the 'error' could well be eliminated by adjusting the volatility input to the implied volatility, I think this actually indicates that I don't understand the logic of comparing these two volatility and therefore concluding that implied volatility is trading cheap in your spreadsheet.

Thank you very much for your enlightenment!

Cheers!

Liming
27/09/2009

 

[David Harper CFA FRM]

Hi Liming,

I think your logic is sound! My XLS may be confusing you, sorry
... because I totally agree with the impossibility of comparing the one implied volatility with other implied volatilies. I mean, as you know, there is a different implied vol for each different strike & term (i.e., the implied vol surface), but I agree, for a given strike & term and for a *given model,* there is only one implied volatility. (also, ignoring bid-ask)

(but as a caveat, model selection can explain a difference, right? For example, I may use the plain-vanilla Black-Scholes Merton to figure the one "correct" implied volatility but you may use some enhanced version/variaion of BSM to produce a "different" or "superior" implied volatility .. this is why i try to stress in the tutorial that implied volatility is a function of the model ... we might go so far as to say that, given your point [i.e., only one implied volatility can be solved] implied volatility is inseparable from model risk!)

...so my view would be that we could discuss/debate the different implied volatilities produced by different models
...but, okay, assuming we use the same model (i.e., traditional BSM), given the same inputs, we must get the same implied volatility.

I think you refer to the difference between implied volatility versus realized volatility.
e.g., if you price the implied volatility of an option at 20% today (T0), but you think the market is underestimating the volatility, maybe you want to "go long volatility" by purchasing the option (or for that matter, arguably a purer volatility trade would be a long straddle), then your view is that the market is trading volatility too cheap and you hope to profit on greater volatility. So, after some time goes by (so I think time is the key dimension: realized volatility has no meaning without time going by!), if the realized volatility is higher than the implied volatility, your position will gain

so i think I agree with you: under same assumptions (i.e., same model, same strike, same term, ignore bid-ask), there is only one implied volatility. Then the idea of a "rich or cheap" volatility is a viewpoint about the future realized volatilty versus the implied volatility (which might be informed by an historical average; e.g,. average vol = 20%, implied vol = 30%, so you think it's "rich" but only time will prove the point.

David