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Hi,I'm having trouble understanding (or getting to work) Haug's implementation of the Curran approximation of Asian ARO options. (pp197-199, Option Pricing Formulas, 2007).Specifically, what parameters should you pass when you have passed a fixing period (m > 0) ? Continuing Haug's table 4-27 example, suppose we have an ARO option sampled once a week for half a year - 27 sampling points - and we are one week into the sampling period, ie m = 1.Alternative: # t1 (time to first fixing) should be negative - eg -1/52 for one week ago# T should be positive - eg 25/52 for 25 weeks until expiry# m = 1, one fixing has been observed# n = 27, there are 27 fixings in totalThe above is the only way (that I have thought of) to get dt = (T - t1) / (n - 1) = 1/52 as required. Haug's spreadsheet suggests the above but t1 is time to next fixing, in which case dt reduces.However, then many other things break, the first of which being (in the first loop)# vi = v * Sqrt(t1 + (i - 1)*dt)since t1 < 0 so the Sqrt explodes.Alternatively, if we say # t1 (time to next fixing) = 1/52# T (time to expiry) = 25/52# m = 1# n = 26 fixings remainingthen an expression like SA > n/m * X does not make sense (since n must here be the total fixings, not remaining).The final alternative is to take abs(t1) whenever it appears with a volatility term, but I'm reluctant to make such an ad hoc change without properly understanding what is going on!All help appreciated!!

Thanks - great explanation, I'll give it a bash.It's still an open question as to whether there is a problem with the code in Haug - as far as I can tell it tries to handle ARO's in the fixing period also. Maybe if the Collector is lurking he can confirm or deny?If I come up with anything I'll keep posting...

I wouldn't change "n" in your concrete example below, i.e. I would taket1 (time to next fixing) = 1/52T (time to expiry) = 25/52m = 1n = 27 (instead of 26)Note however that you need to adjust the initial strike of the option (see Haug p. 196) in order to make the valuation in this case (since averaging has already started).

in the formulas, shouldn't there be a square root for sigma_x_i definition p196?

outrun, your derivation that makes sense to me,doesn't agree with the replacement strike in Haug p196He doesn't even say that the new asian price (with replaced strike) should be multiplied by (n-m)/n