VaR on forward contracts

Question

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.

Answer 1

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.

Answer 2

What you described will not work for calculation of VAR (if I understood correctly that you intend to work with the time series of forwards directly).

You need to create a historical sample relative returns on the underlying, in fact vectors of absolute or relative returns for all factors mentioned in another answer, i.e the vector may contain (rel underlying returns, relative or abs returns on rates, conv yield etc). You generate 250 such vectors from history and term of those returns should match the term of VAR you are computing.

If you originally have daily time series of the factors and need, say, weekly VAR, you will need to construct weekly non-overlapping returns, so you will need 5 years of data; otherwise you will have to deal with positive autocorrelation overlapping returns will introduce.

Then you apply the change vectors to your initial MD vector, generate MD scenarios and plug them into the forward pricer, accounting for the shorter time till expiry (by the VAR terms).