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I would like to price an Asian Call Option with 0 carry using the formula by Turnbull and Wakeman in the book of Haug.

Formula1

formula2

formula3

I found a package in R, fOptions, that has already implemented the function: https://www.rdocumentation.org/packages/fOptions/versions/251.70/topics/AsianOptions

The problem is that in the book what the authors of the package describe as tau is calculated automatically as t1 and if it is equal to 0 it would mean that the option matures at exactly the start of the average calculation period. In the example of the R function the tau is set to 0, but the time to start of average period and time to maturity are different, which for me makes no sense.

The following are the inputs of the function as the book implements it. Notice how t1 (the tau of the R function) is calculated and not put as input.

Inputs_Asian_Book

Does anyone have an idea as to why there is a difference in the implementation and what it means ? How can I use the R function ?

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