I am currently writing a paper examining two models for pricing options on WTI Crude oil futures, and I want to backtest hedging strategies from both model and compare them against each other.

However, I am having some trouble visualizing how the backtest should look like. My initial thought was to implement a traditional delta hedge but as the underlying is a futures there is no cost of buying/selling the underlying (if we disregard transaction costs etc).

How can I implement a meaningful hedging strategy using futures and options on futures?

EDIT: Any links to papers on this topic is also greatly appreciated!

Thanks and apologies if the question is unclear.

  • $\begingroup$ "there is no cost of buying and selling futures" I know what you mean, but: Every day there is a Profit or Loss for the option and for the Future. Your job is to make sure these two offset each other as much as possible. And the Delta Hedge is the way to do it. $\endgroup$ – noob2 May 22 at 18:30
  • $\begingroup$ The Delta for Options on Futures is derived from the Black-76 model en.wikipedia.org/wiki/Black_model , which is slightly different from the Black-Scholes model used for stocks. But the rest is very similar. $\endgroup$ – noob2 May 22 at 19:30
  • $\begingroup$ Hello, and thanks for your reply! You are of course completely right. Thanks a lot, I will look into this. $\endgroup$ – Vetlekos May 22 at 20:04

Most of the academic papers I have seen use simulated data rather than backtesting on historical data because historical data only gives you one price path and the true underlying dynamics can not be known for certain. I think you are looking for a paper like: Which Free Lunch Would You Like Today, Sir? Delta Hedging, Volatility Arbitrage and Optimal Portfolios. In this paper the authors examine the differences in return/risk profiles when hedging with a delta calculated from different implied vols. For your paper I would recommend thinking about what the two models assume about the underlying and where that difference would be most extreme. For example, if the main difference in the model is related to skew then run a simulation or backtest comparing the return distribution of a delta hedged fence (long otm call and short an otm put hedged with the delta).


Adding on to @noob2's answer, there is both a implied probability of a margin call and changing liquidity requirements when trading oil futures.

Backtesting a strategy that involves hedging using futures should take these into account

  • $\begingroup$ Dear Kareem, Thanks a lot for your reply, very interesting. Do you perhaps have a reference or a pointer to where I can learn more about the implied probability? Many thanks $\endgroup$ – Vetlekos May 22 at 20:06
  • 1
    $\begingroup$ Not only that; you should probably also take the margin payments into account and the cost of it. $\endgroup$ – simsalabim May 28 at 14:17

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