Hi,I have the following question on asian options:A lot of options traded in the commodity markets are discrete arithmetic average options. Such options are traded also on the London Metal Exchange, where they are called TAPOs ("Traded average price options").Based on discussions I've had with some people, I've been told that the model LME uses is described in the paper (see p.13-17):http://www.lchclearnet.com/Images/LME%2 ... 424.docThe model is based on Turnbull-Wakeman-Levy approaches. It seems to me, that one main difference - compared to the academic literature - occurs for average options, for which the averaging period has already started. In such cases, the academic literature requires an adjustment of the original strike of the option, in order to account for the fact that some values entering the average are already known (see books by Haug, Hull, etc.).It seems to me that the LME model does not take such a strike adjustment explicitly into consideration (however it accounts for that in calculating the volatility (see paragraph 5.2 in the above document)). Did you had any experience with that?Thanks in advance for your comments,Paul

Hi Paul,what you have to know about the Turnbull-Wakeman and the Levy approaches that they approximate the distribution of the arithmetic basket by a lognormal distribution. However, we know that the sum of lognormal randoms is not lognormal, but if these lognormal randoms are highly correlated with each other and their volatilities are closely the same then the sum of randoms is approximately lognormal. Thus the approximation error of the approaches above is usually acceptable for Asian options.Nevertheless, if the averaging period has already started then the volatilities are inhomogeneous, the volatilities of past fixings are zero. Moreover the correlations between the fixings are decreasing as the option is maturing. Therefore, if you do not deduct the past fixings from your strike, the mentioned approaches may cause significant approximation error.If you use these approaches you should clearly deduct the past fixings from the strike in order to reduce the approximation error in your option price.Best regards,Peter

what is this approximation in the note?At first sight it looks different from Levy and different from Turnbull&WakemanOr am I just not looking well enough?

The LCH model also tries to approximate the sum of lognormals by a lognormal.This is done by matching the first two moments (by adapting the volatility). The notations are a bit complicated in the LCH paper. If the option is BEFORE the averaging start, it seems to me that the above results are consistent with T&W / Levy. However, once the option is already IN the averaging period, the approaches are not exactly the same. The model described in the LCH paper only adjusts the volatility, while in T&W and Levy the original strike price is also adjusted.

LCH Tapo model is consistent with Levy (log-normal moment matching). There are two ways to go when pricing Asian options within the averaging period (at least within this framework):1) Adjust the strike and treat this as a "new" option.2) Incorporate the correction for the fixed portion of the average in the calculation of vol of the average.If applied consistently both approaches yield exactly the same result. LCH uses option 2.