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I am trying to calculate a historical VaR, let's say on a forward contract of Gas that has a delivery in December 2022 ( begin delivery = 1st December 2022 and end delivery = 31st December 2022). Having calculated all my returns for the last 250 trading days, I want to know which return I will apply to my current position ? For me, it seems to be two obvious solutions :

  • Relative return : it means that knowing that as of today, December is 4 months away, for each return date, I will consider the M+4 return.
  • Absolute return : it means that, for each return date, I will apply the return computed for December 2022 forward contracts.

Thank you for your help.

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  • $\begingroup$ The price of future contracts/options should already incorporate the time effects, simply by the argument of no arbitrage opportunity. So you just need to compute the absolute return for each date and they should be your pnl $\endgroup$
    – The One
    Aug 18, 2022 at 15:51

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It is the relative return you should be computing if you want to assess the risk of holding your current contract to maturity. I assume you have been able to extract past 1 year of data of all your risk factors (Spot, Convenience Yield, Storage Cost, Discount Rate). You would have done this by modelling your past 1 year data into risk factors that could be used to price your contract today. Historical Simulation VaR is not assuming you hold the same contract through the last 250 days. It is a simulation assuming you've got the same instrument of the same trade economics you hold today.

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