Hi,An interesting question came up recently regarding crack spread options. Should the sum of the deltas of the two legs add up to exactly zero?Thanks in advance.

Don't think I was clear on this... the point that was made to me was that, since one can hedge crack options with the spread (which trades), it must hold that the sum of the leg deltas should add up to zero. If this is true, then we must model such options as function of spread, and any model which models each leg separately will not work (since it doesn't guarantee sum of leg deltas = 0 unless certain conditions are met).I am looking for opinions - for and against this argument. Thanks v much.

Why? (I need the argument!).

I am not sure if I understand your question. I assume that you are asking if the two deltas sum to zero at the current market crack spread.Without doing any math, I would think that the model implied crack spread should be close to the market spread for the arbitrage reasons suggested (but only if both legs and the spread trade), though it is not a given and the model would have to be calibrated to the market.I don't get why this means we need to look at the spread and not the individual legs. It would simply be a matter of calibration (I think). The underlying issue will be the distribution of the spread. Modeling the spread directly will, generally, give you a smoother distribution for the spread. Modeling each leg seperately will give you a less well behaved distribution.Personally, I have had some success by paying attention to the distribution of the spread and modeling it directly.

Hi Beachcomber,The question is about whether the two deltas are *supposed* to sum to zero. If this statement is true (and I dont know why it should necessarily be the case), then models of the crack spread alone would need to be considered.To make this clearer, consider a model in which each leg is modelled separately and we specify a correlation between them. Let's assume no vol skew exists for each of the leg components (say, HO and CL) for the moment. We calibrate this model to the HO and CL forwards and atm vols. Since this is a lognormal model it's easy to price the crack spd option by reducing it to a 1D integral (by conditioning on 1 factor). We can then work out the leg deltas, and it is easy to see that unless the vols are equal, then will not add up to zero. This means that this 2-factor model is not going to work, *if* for some reason we can justify that the two deltas add up to zero.

It's a strange question to me, I never think to delta like this in commodities: yetanotherquant you are perhaps from equities?What i can simply observe is that the crack spread itself has not a zero delta:- the delta is <> zero in terms of lots: brent-gasoil crack is 3 lots brent and 4 lots gasoil- the delta is <> zero in terms of dollar equivalent: that difference is indeed the crack spread vale

commoddity - I mean leg deltas in barrels.. one would have to first convert HO price (from cents/gallon) into the units of CL price ($/barrel) and then compare, so that one is comparing apples to apples.outrun - indeed, a spread by itself will not give a unique option price, but I can't see how that answers my question.Following up on my previous example, if one modeled the crack spd option using fwd spread (gotten from the diff between fut prices of underlyings), one would only get back the delta wrt the spread. But one can get the leg deltas by multiplying by 1 and -1 (and by notional, and converting to appropriate units), so by design the leg deltas (after converting back) sum to 0.I have asked this question of a couple commodity professionals (1 oil trader, 1 strat) - the oil trader said: sum of leg deltas = 0, and the strat said sum of leg deltas <> 0. I believe the latter, but am looking for an argument for it. If easier, you can pm me.Thanks v much.p.s. I am from commodities.

>a spread by itself will not give a unique option pricewhy not - if the option depends only on the spread?

From a traders standpoint, the difference between whether the deltas net to zero or not is very small. A quant would argue that the deltas should not sum to zero for all the reasons stated but a trader would delta hedge a crack option using equal volumes on each leg. Most practicioners use single factor models for simplicity sake. Your question is basically only relevant to a quant.

As a trader, if you had an ATM straddle position on such a spread option, what delta hedge would you put on it?QuoteOriginally posted by: AT2KMFrom a traders standpoint, the difference between whether the deltas net to zero or not is very small. A quant would argue that the deltas should not sum to zero for all the reasons stated but a trader would delta hedge a crack option using equal volumes on each leg. Most practicioners use single factor models for simplicity sake. Your question is basically only relevant to a quant.

To answer my own question, the reason for asking it was that once I was helping out someone with location spread options.As per this discussion the debate over whether to model the spread as an independent entity or as two correlated process was raging,particularly as this guy had a straddle position. Naturally if you go down the Kirk/correlated lognormal processes route you get the counterintuitiveresult that the market tells you to short both markets on a long option position. He told me that was ridiculous and he couldn't trust any model that came up with those hedges. My response was to say, the question reduces to whether, if the market approximately doubled but kept the same spread, would his options be worth the same, or more. In that light shorting both, or having a net short position didn't seem to be so unwise. QuoteOriginally posted by: twAs a trader, if you had an ATM straddle position on such a spread option, what delta hedge would you put on it?QuoteOriginally posted by: AT2KMFrom a traders standpoint, the difference between whether the deltas net to zero or not is very small. A quant would argue that the deltas should not sum to zero for all the reasons stated but a trader would delta hedge a crack option using equal volumes on each leg. Most practicioners use single factor models for simplicity sake. Your question is basically only relevant to a quant.