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I am trying to compute the implied volatility of the OBM contract (on Euronext), using R, and I was wondering if, for the time to maturity, I should put the time until the contract expires or the time until the last trading day of the option. There is a difference.. For example : an option expiring on the 10th of March can be traded until February the 15th of the same year.

Thank you in advance

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Volatility time to maturity should be until the option expires. Also be careful that these are options on futures so pricing should be with zero drift for the underlying (see e.g. Black 76 formula).

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  • $\begingroup$ Thank you for your reply, I am new to finance and it is the first time that I read about the Black 76 model. But I'm a bit confused, does that change the implied volatility formula? $\endgroup$ – Narjems Oct 29 '18 at 20:07
  • $\begingroup$ As you know there is no "implied volatlity formula" (it is an iterative process), but yes it is different. Some people write separate code commoditymodels.wordpress.com/2012/07/28/… , but it is also easy to write one routine that can handle the BSM, BS and Black76 cases interchangeably because they are so closely related. $\endgroup$ – Alex C Oct 29 '18 at 21:47
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    $\begingroup$ If you already have available a function that computes the Black & Scholes implied volatility (typically implemented using a root search algorithm such as Newton-Raphson to find the volatility such that the recomputed price matches the inputted price, as mentionned by @Alex C), then you can use it for Black 76 by setting the dividend rate equal to the interest rate. This is because the risk neutral drift for the underlying is $E[dS/S] = (r - d) dt$ where $r$ is the interest rate and $d$ is the dividend rate, so that taking $d = r$ will ensure that $S$ has zero drift. $\endgroup$ – Antoine Conze Oct 30 '18 at 10:03
  • $\begingroup$ Thank you @AlexC and Antoine Conze. Great explanations $\endgroup$ – Narjems Oct 30 '18 at 15:00

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