# Implied Volatility for Asian option

I am new to the topic of Asian options. Assume I want to price an Asian put (fixed strike, discrete average) in the Black Scholes world. I know implementations to calculate the value but what is the best way to find the implied volatility parameter? Is there a usual way to derive it from the option market of plain vanilla products, e.g. European calls or puts of a certain range of maturities?

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## 1 Answer

The easiest way is to use single-expiry volatility that you would get from your volatility surface. It is usually good enough for government work (e.g. to get a sense if you are getting raped by a dealer or to understand your vega risk).

A better way is to use local volatility model and the whole volatility surface up to the date of expiry. There is also a bunch of semi-analytical approximations that use weighted volatilities up to there expiry date. Unless you are a dealer and trying to quote these in competition, you don't need to bother with these.

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By the first solution. Do you mean that e.g. if I price an Asian put with 12 months maturity and strike ATM then I take the 12 month maturity ATM volatility of e.g. a European call? Concerning the 2nd point: do you know a good reference (theoretically appealing and pracitcally relevant)? This would be nice ... – Richard Oct 31 '12 at 16:54
Yes, you would use the volatility for the same strike and same tenor. For the second one, I thin this is what your are looking for: www.dm.unibo.it/~pascucci/web/Ricerca/PDF/39_FPP.pdf – Strange Oct 31 '12 at 21:02
I have browsed through the paper of your link. I find it theoretically very interesting. I just wonder whether there is some other more applied article...thank you – Richard Nov 2 '12 at 18:28
Is local vol used in practice for Asian options? I was under the impression most dealers still used analytic approximations. – user3316 Nov 26 '12 at 2:03
There are some semi-closed form solutions to Asian options. The stupid things trade so tight that it's almost impossible to make out if you are off because of the vol surface differences, business time calculation or modelling differences. I have been to a place where Asians where calculated on local vol model as well as to a place where we used some sort of moment matching model - guess what, both places we some times where off market, except in case of local vol model my junior had to stay till 9 pm to get the P&L and risk for the book. – Strange Nov 26 '12 at 2:09