a Bachelier model vs shifted Black model

[frolloos]

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

[nikol]

@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]

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.

[vertigo]

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

[ronin]

> 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.

[nikol]

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]

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.

[nikol]

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]

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

[nikol]

"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.