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SWilson
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Joined: February 13th, 2018, 5:27 pm

### Negative forward futures prices

It may be probable that we will have a forward month for Oil with a negative futures price, Black cannot compute the time value of an option due to the log of a negative being undefined.  Please help.

Alan
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### Re: Negative forward futures prices

For positive strikes and negative futures prices, since the option is out of the money, the time value is the quoted value. For negative strikes and negative futures prices, the time value is the quoted value less the amount, if any, that the futures price exceeds the strike.

gelfand
Posts: 144
Joined: July 14th, 2002, 3:00 am

### Re: Negative forward futures prices

Should oil futures prices be modeled as an arithmetic brownian motion rather than a geometric one? Maybe they are arithmetic once the price falls below a certain price level?

pcaspers
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Joined: June 6th, 2005, 9:49 am

### Re: Negative forward futures prices

Shifted Lognormal with lower bound = max storage cost?

SWilson
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Joined: February 13th, 2018, 5:27 pm

### Re: Negative forward futures prices

Shifted Lognormal with lower bound = max storage cost?
That's an interesting thought provoking approach.  Luckily, we're not looking at any more negative prices for future deliveries, so for now, threat neutralized,  but I would like to update my model for this if it happens again.

gelfand
Posts: 144
Joined: July 14th, 2002, 3:00 am

### Re: Negative forward futures prices

Shifted Lognormal with lower bound = max storage cost?
That's an interesting thought provoking approach.  Luckily, we're not looking at any more negative prices for future deliveries, so for now, threat neutralized,  but I would like to update my model for this if it happens again.
The cost of storage is also variable. A shifted lognormal model with lower bound of say -30$/barrel would imply that the oil futures prices has low volatility in dollar terms as oil approaches -30, but in fact the$ volatility would be high in such an unusual situation. Look at how May WTI oil futures traded before expiring.

gelfand
Posts: 144
Joined: July 14th, 2002, 3:00 am

### Re: Negative forward futures prices

April 21, 2020, 4:46 PM EDT Updated on April 22, 2020, 5:12 AM EDT
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Traditional options models assume prices can’t go below zero
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Wall Street scramble to recalculate positions adds to mayhem
...

CME Group Inc. said late Tuesday that the clearing house will switch the options pricing and valuation model to Bachelier -- a model named after the famous French mathematician -- to accommodate negative prices in the underlying futures and allow for listing of options contracts with negative strikes for a certain set of crude oil and energy products. The change is effective Wednesday and will remain in place until further notice.
ICE Brent options contracts also will require a switch in models to enable trading of negative strikes if there’s demand to do so, the company said.
There has been a surge in interest in 50-cent puts for June WTI -- which traded as high as $3.90 on Tuesday, implying that traders are already working on the assumption that June WTI futures could turn negative. “From a market maker perspective, particularly those sitting at a flow trading desk or a major, their assumption, especially if you’re young and haven’t experienced any major market events, the assumption is that$0 was always the minimum,” said Michael Corley, president of Mercatus Energy Advisors. “That’s not the case anymore.”

SWilson
Topic Author
Posts: 67
Joined: February 13th, 2018, 5:27 pm

### Re: Negative forward futures prices

Thanks.  Yeah we will probably toggle to Bachelier when the situation arises.

bearish
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Joined: February 3rd, 2011, 2:19 pm

A long time ago, I was encouraged to take on a leading quant role in one of the major financial players in the commodities market, with a particular strength in energy derivatives. I demurred on account that it would seem to be crazy to apply simple financial market models (that I knew something about) to things with finite supply, non-trivial storage cost, location specific pricing, no free disposal, and a small number of players with real market power. Seeing a discussion fifteen years later whether one should switch from Black to Bachelier after a $40 drop in the near WTI contract price suggests that a lot of thoughtless modeling is still going on in this space. kshemyakin Posts: 11 Joined: October 21st, 2013, 4:45 am ### Re: Negative forward futures prices Thanks. Yeah we will probably toggle to Bachelier when the situation arises. Hi! We've also come across Bachelier. Hoewever, does Cox-Ross-Rubinstein work in negative environment (both negative rates and negative prices)? Or does it also assume lognormality like BS (i.e. that prices cannot be negative)? Thanks “Real creativity won’t make things more complex. Instead, it will simplify them.” SWilson Topic Author Posts: 67 Joined: February 13th, 2018, 5:27 pm ### Re: Negative forward futures prices A long time ago, I was encouraged to take on a leading quant role in one of the major financial players in the commodities market, with a particular strength in energy derivatives. I demurred on account that it would seem to be crazy to apply simple financial market models (that I knew something about) to things with finite supply, non-trivial storage cost, location specific pricing, no free disposal, and a small number of players with real market power. Seeing a discussion fifteen years later whether one should switch from Black to Bachelier after a$40 drop in the near WTI contract price suggests that a lot of thoughtless modeling is still going on in this space.
For this particular application I am only looking to use a simple financial market model for a fair value approximation.  However, I do agree with your assessment in general.  The participants on this board all have different needs and levels of sophistication they are trying to achieve.