Correct modelling of this is interesting for both options and futures pricing, as average process has obviously less volatility than "regular" process. How much less? Well, apparently I fell asleep during a class because I have no recollection of the formula until I recently researched it.
B(t) is ABM, then
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjxu_OQ6SpRTU_m6vsgo8PnomlIBsKGnBrySKJuf9B2Q32M0q-s4ind2qUat1XnTxcfiyqHzZNN-ZOXY_tqCieQ7gPDAM9Qbn_Zb8SqP42cdb3lvPe3ZIpl5qTbrKQM_FG5bcz6zxbXKnN1/s1600/CodeCogsEqn+(5).gif)
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgDLxFokvghsYqCGibl7d1OrHp542LFOdjT0aXNLAiqGKcyqYXclhjCm7wIKHYyEBiLLIm4mrJo-vVy85MngsXzJUfpRj1O4l6imQ3xhQQLIVjrvvyl1jNz-Axi3ZjWNSIDgTdoIwXB-GX7/s1600/CodeCogsEqn+(4).gif)
In simple terms, average has 1/sqrt(3), or about 58% of volatility.
Simple example: assume BTC/USD volatility of 100% per year. Expected volatility over 30 days should be sqrt(100 * 100 * 30/365) = 28.67%. However if the contract settles to the last day's average, for options pricing we should use volatility of sqrt(100 * 100 * 29/365 + 100 * 100 * 1/365 / 3) = 28.35%, slightly lower.
In conclusion: average settlement - interesting, but of little practical importance from pricing perspective.
P.S. Re: Atlas ATS - could not get their API to work, waiting for LedgeX.
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