In considering the value of an Asian call of the form max(0, AVG - X), there is much literature out there on how to compute prices.Many of the approximations in the literature compute an approximate value of the Asian call by, conditional on a volatility for the stock price, calculating the moments of the average stock price. However none of the literature deals with the related question of how to choose the volatility parameter appropriately.If you are valuing an Asian option with a long Asianing period, then the shape of the volatility term structure must be important in determining the parameter. Alternatively one could go directly to local or stochastic vol models, but I don't get the sense that many desks are doing that in practice.Does anyone have any thoughts or references?

It sounds like, ideally, you would like a formula that converts the ATM implied vol. term structureinto an effective GBM volatility. Then, you insert that effective vol. into the GBM Asian solution to get a value.If this procedure were to work generally, it would imply that the volatility skew was largely irrelevant foryour long-dated Asians. Now, no one on a message board can tell you if this is a good approximation or not.After all, we don't know what you are going to do with these options, what kinds of valuation/model errors you cantolerate, etc. Same problem if someone tells you what other desks are doing. But you can test the idea with models. First, set up a purely deterministic variance process V(t) such that sig_imp(T) = [int(0,T) V(t) dt/T]^1/2, where sig_imp(T) is a market term structure with a lot of variationbetween very short and very long-dated vanilla options. Now value the long-dated Asians with V(t). Now set up a stoch. vol. model process V(t) with dV = b(V) dt + a(V) dW(t), whereb(V) is chosen to match the term structure above, and a(V) and the correlation parameter is chosen to have a decent fitto the option chain, perhaps ignoring very short-dated stuff. Re-price the Asians under this model.See if the skew (i.e. a(V) and the correlation parameter) mattered significantly to your pricing.Repeat for other hypothetical term structures that might appear in your particular market.Anyway, that's what I would do to either justify some trader's rule-of-thumb -or- show how dangerous it was.Finally, even if the second model looks good, eventually the options priced off of it will mature. If youuse that model to mark-to-model your very short-term stuff, you have then forgotten that your original modelwas never calibrated to very short-term options. Anyway, my two cents.

Hi Alan,It is hard to imagine anyone could have summed up the problem better than you did. In fact, I did a less robust variation of what you describe below already and here is what I found. The skew does matter. Stochastic vol models produce different answers than GBM models almost irrespective of how one chooses the volatility for the GBM diffusion.Trouble is that when I compare results of different models to marks on actual trades, they much more closely resemble one of my "test" ad-hoc GBM approaches (such as, (a) average the BS volatilities for the vanillas maturing on the averaging dates, plug into closed form (b) compute forward vols along those same averaging dates and plug into MC pricer, etc). So while it is true that I "would like a formula that converts the ATM implied vol. term structure into an effective GBM volatility" ... it is only true because to me it appears that others are doing this, so if for nothing other than consistency, I would like to as well, or at least to know if the market has adopted some kind of standard approach to pricing this option.

Stylz,if i remember correctly the problem you are describing, i.e. computing an effective GBM volatility from a vol term structure, was covered in the "Asian Pyramid Power" paper by Espen Haug et al.

QuoteOriginally posted by: StylzHi Alan,It is hard to imagine anyone could have summed up the problem better than you did. In fact, I did a less robust variation of what you describe below already and here is what I found. The skew does matter. Stochastic vol models produce different answers than GBM models almost irrespective of how one chooses the volatility for the GBM diffusion.Trouble is that when I compare results of different models to marks on actual trades, they much more closely resemble one of my "test" ad-hoc GBM approaches (such as, (a) average the BS volatilities for the vanillas maturing on the averaging dates, plug into closed form (b) compute forward vols along those same averaging dates and plug into MC pricer, etc). So while it is true that I "would like a formula that converts the ATM implied vol. term structure into an effective GBM volatility" ... it is only true because to me it appears that others are doing this, so if for nothing other than consistency, I would like to as well, or at least to know if the market has adopted some kind of standard approach to pricing this option.Thanks for the compliment. If quotes and trades are uniformly away from your SV model(s), then the conservative conclusionis that there is a problem with all the models. One thing I would check carefully is the detailed term structure of implied volatilitiesin the models;. If you see structure there not present in the market, then this may be the source of the problems withthe model prices.

Hey esve and alan for the replies.esve, Thanks for that. Any links where I can find the paper? I was not a Wilmott subscriber in 2003. Thanks

I found the paper in the "Derivatives: Models on models" book, so unfortunately I don't know if it is available on the web.However, I think there is a video recording in the Articles section on this site.