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pj


Total Posts: 3555
Joined: Jun 2004
 
Posted: 2020-06-11 15:18
Ladies and gentelmen,

All the developers are adamant that the negative prices
in commodities do not exist.

So the question arises,
how could one approximate the Bachelier model with shifted Black model (i.e. add a shift to the modeled commodity)?

Any ideas, thoughts, references?

< EDIT > to the attention of them, nitpickers. I mean modeled price.

The older I grow, the more I distrust the familiar doctrine that age brings wisdom Henry L. Mencken

deeds


Total Posts: 481
Joined: Dec 2008
 
Posted: 2020-06-11 15:22

A significant series in literature from a couple of angles around implying three moment shifted lognormal (in the manner of Turnbull Wakeman for Asians) for baskets, spreads and for negative rates.

I know you have great resources, lmk if you don't see

pj


Total Posts: 3555
Joined: Jun 2004
 
Posted: 2020-06-11 16:22
This one seems to be promising.
Walter Schachermayer And Josef Teichmann how close are the option pricing formulas of Bachelier
and Black–Merton–Scholes?

But maybe something more down to Earth?

@ deeds, thank you, will take a look.
(Although I have been burned on
the normal approximations of lognormals)

The older I grow, the more I distrust the familiar doctrine that age brings wisdom Henry L. Mencken

deeds


Total Posts: 481
Joined: Dec 2008
 
Posted: 2020-06-11 16:55

Thanks, pj, possible to share details?

bad fit in a range or more global problem?

pj


Total Posts: 3555
Joined: Jun 2004
 
Posted: 2020-06-11 17:12
If I recall well, bad fit.
Finally we yielded and integrated everything numerically.

The older I grow, the more I distrust the familiar doctrine that age brings wisdom Henry L. Mencken

nikol


Total Posts: 1230
Joined: Jun 2005
 
Posted: 2020-06-11 22:01
Price of commodity itself is positive (thx God). The negative is price of obligation to deliver, where storage_price exceeds sell_price, so you may think of something like:

delivery_price = sell_price - storage_price < 0

My point is that the price of commodity at delivery point (DDP) can be broken down into chain of deliveries in accordance to Incoterms (https://en.wikipedia.org/wiki/Incoterms)

Every step like load, offload, transshipping, transporting, storage etc. adds a bit to the final price. If you agreed to deliver at 100 and locked that price with futures and all your contractual obligations suddenly popped up above 100, then you have to pay to get rid of the product, hence negative price.

Bachelier and Black are saved!

deeds


Total Posts: 481
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Posted: 2020-06-12 10:20

Thanks, have looked at incoterms

...confirming understanding...commodity price is modeled as a stochastic process separately from costs of carry. In the equation above is storage_price modeled as a fixed amount for each contract?

nikol


Total Posts: 1230
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Posted: 2020-06-12 13:52
I never modelled these costs, so cannot say.

However. IMHO. it should be dynamic. Look as an example storage costs around Oklahoma when prices became negative. To make it properly designed you have to account for demand and available capacity. This is what happened - oil was supplied at usual volume speed, while its consumption completely ceased, so the storage capacity depleted and was in high demand. Perhaps, it should be some model of "message delivery in the pipeline system with random intensities and limited capacity"

pj


Total Posts: 3555
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Posted: 2020-06-12 14:18
So you propose to model the storage costs as well.
Should I use another Black Scholes for that? Tongue out

The older I grow, the more I distrust the familiar doctrine that age brings wisdom Henry L. Mencken

nikol


Total Posts: 1230
Joined: Jun 2005
 
Posted: 2020-06-12 14:54
Whatever you please. :)
You should model reality. Otherwise you will end up in the imaginary world with negative commodity prices.

frolloos


Total Posts: 126
Joined: Dec 2007
 
Posted: 2020-06-12 16:02
I don't know anything about commodities but just saw this paper which may be of interest to you:

https://arxiv.org/pdf/2006.06076.pdf

No vanna, no cry

nikol


Total Posts: 1230
Joined: Jun 2005
 
Posted: 2020-06-12 16:39
@froloos

Interesting approach.

I disagree with footnote about Russian hotel. That example does not mention repo contract hence the whole story is unrealistic. The recent oil story is better one. Or even epic long lasting story with negative rates :)

frolloos


Total Posts: 126
Joined: Dec 2007
 
Posted: 2020-06-12 17:08
I don't know much about Russian hotels either :) The only time I was at a Russian hotel was before I met my wife, on a typical cold Moscow winter night (pre global warming). There was a good party, and the hotel seemed far from dilapidated, although I suspect there were some repo transactions going on, but now I'm really going off topic.

No vanna, no cry

vertigo


Total Posts: 9
Joined: Dec 2015
 
Posted: 2020-06-17 19:11
let z by the price of the underlying asset ... then we have the classical lognormal model:

dz=v_ln z dw

where v_ln is the lognormal implied vol

we also have the classic normal model:

dz = v_n dw

where v_n is the normal implied vol

now consider a new model, where we have

dz = d(z-a) = (z-a) v dw

where v is a (new) implied vol and a is some positive number.

this is the shifted lognormal model. z has the solution

z_t - a = (z_0-a) exp [ v*w_t - 0.5*v^2*t ]

the price of the european call E[(z_t-K)^+] can then be computed in the standard manner

... maybe one day ...

ronin


Total Posts: 607
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Posted: 2020-06-17 20:28
> https://arxiv.org/pdf/2006.06076.pdf

Richard Martin is a smart guy. I knew him back in the day.

But this is still a one factor model, or two factor if you incorporate the convenience yield. The oil curve has more than two factors. Also, how do you get the vol and correls for the convenience yield?

Last time I was pricing oil options, we were actually doing it as a multifactor curve. Each future was lognormal with a flat forward, and the rolling contract was piecewise constant interpolation between roll dates. Vols came from options on futures, and correls were bootstrapped from swaptions. Basically, LMM for commodities.

@pj, I guess something like that would still work, if you just make the futures normal or shifted lognormal instead of lognormal.

"There is a SIX am?" -- Arthur

nikol


Total Posts: 1230
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Posted: 2020-09-04 16:47
Ah. Why all this.. This problem is "simpler" *)

Remember that actual futures pay-off at maturiy is = UnderlyingPrice - StorageCost


StorageCost depends on demand vs supply of warehouses, so one has to monitor it. If there are warehouses of N tonnes and their discharge falls below this threshold, then the StorageCost **jumps*. So, you need to know current WH capacity inflow (outstanding futures) and outflow (e.g. proxy of season/economy?).

Similar with demand vs supply of the underlying - if demand < supply, then UPrice falls.


If StorageCost **jumps** through the roof or UPrice plunges, then we easily get F < 0.

*) This problem is at least shifted to different problem to find data about demand/supply.

Patrik
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Posted: 2020-09-04 17:58
In practice I've never had any reason to really care about modelling commodity spot prices in the setting of thinking about derivatives - only the futures prices are required. And as futures prices can be (and has been) negative there's nothing wrong with a Bachelier approach. What @ronin describes is still the general approach in many shops that care about a more self-consistent vol models and non-vanilla options (often with less factors than 1 per futures expiry though), but lots of shops don't really have a need for that and trade a lot of simple options with simple models and vol surfaces.

In practice I've never actually met anyone in the commod derivatives space that use spot and abstract convenience yield concepts in an option pricing setting. Obviously physical traders do care about spot prices, but they don't tend to get involved with options pricing so hence little explicit modelling tying spot and futures together.

Capital Structure Demolition LLC Radiation

nikol


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Posted: 2020-09-04 19:59
Perhaps nobody tried to sell options to phys.traders, so they dont use them.

For me it is the question of how to model the reality and not of how to approximate the movement of pnl.

Patrik
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Posted: 2020-09-04 20:44
There are plenty of options involved in physical trading, but they're not always of the dynamic hedging variety. Also, there has at least historically been a bit of a culture of not exactly flagging there's optionality around (e.g. it may not be represented in systems or M2M etc). If you as a physical trader get some "cheap" (often unquantified) optionality and never make a big deal out of it, then if you make nothing out of it no biggie, if you do you look like a hero - that kind of thing. It's been getting more sorted over time but it's often more primitive (from a models/math/tech perspective) than people from financial markets expect. Not to say that it's primitive overall - plenty of smart people involved, just different.

I guess us commod folks see the question as how to make money more than anything else - and for that the elusive "convenience yield" seems to have no relevance :)

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nikol


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Posted: 2020-09-05 11:28
"Convenience yield" is similar to bond yield - everyone uses it to qoute the price, but it is not a proper risk factor, which can propagate through all kinds of product used to hedge risks.
As example, banks used yield for quite a while, but still were forced (by the need of capital reduction) to switch to IR curves and credit spreads to properly account for fair valuation of cash flows.


Patrik
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Posted: 2020-09-06 23:10
I'm not in FI so wont comment on what a good comparison is - but my point was more that the convenience yield concept is not really used for anything in commodity markets. I've only ever come across it in papers (written by non-commod people).

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ronin


Total Posts: 607
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Posted: 2020-09-08 21:03
It's funny, that one.

It really depends on easy it is to carry the commodity forward.

On one end of the spectrum you have precious metals, which are basically just currencies. The commodity is pretty much never destroyed, it's just all carried from one maturity to the next. The curve moves in parallel, convenience yield is meaningful but it is, for all intents and purposes, zero.

You then go through stuff like base metals and oil. You could carry it, but it's really, really expensive. Carry only serves to impose the contango limit. The curve is like a whip, it jumps around, but nearby expiries are correlated. I suppose you could think of it in terms of the convenience yield, but it isn't particularly useful.

Then softs, livestock and the likes. You can carry it for a short while, but it isn't even theretically possible to carry it for too long. The concept of convenience yield is coming under the strain it was never supposed to bear.

Finally, power. "I'm gonna buy myself some morning power, then pay some convenience yield, and use it in the evening" - yeah, just no.

"There is a SIX am?" -- Arthur

nikol


Total Posts: 1230
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Posted: 2020-09-08 22:09
Conventions play a role in markets.
Everyone trades imp.vols though everyone agrees it is wrong "entity".

Patrik
Founding Member

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Posted: 2020-09-09 09:56
My last try - convenience yield is a concept that has no role whatsoever in commod markets, and that no one ever talks about in these markets Smiley

I'm just trying to make it very clear it is very different to concepts that may be "wrong" in some ways but are still part of markets (usually for good reasons).

It does have a role in some papers and research, but seldom for people actually involved in commodity markets.

Capital Structure Demolition LLC Radiation

Maggette


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Posted: 2020-09-09 19:27
I have been in energy trading (everything but oil....electricity, natgas, emissions, coal....)

With my limited experience, I really dito Patrik.

I worked with energy traders whose official reason of existence was to monetize the optionality inherited in the real generating asset park.

They were smart people with a good feel for the market and a deep understanding of the commercial, regulatory and even technology aspects of their energy market. I learned a lot from them. But after a closer examination it was pretty clear that they didn't even know what a delta is.

A lot of concepts from academia exist under different names or replaced with a simple heuristic though.

Ich kam hierher und sah dich und deine Leute lächeln, und sagte mir: Maggette, scheiss auf den small talk, lass lieber deine Fäuste sprechen...
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