No-Arb range of forwards

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risk taker
Posts: 41
Joined: Wed Aug 10, 2011 12:52 pm

No-Arb range of forwards

Postby risk taker » Mon Aug 13, 2012 1:16 pm

Hi Carol,

As one can only conduct one-way arb for commodity forwards, you mentioned in the book that the market price of a forward contract can fall very far below its fair value. Does this mean that there is NO lower bound on the no-arb range i.e. the forward price can be underpriced but will never be overpriced due to cash and carry arb?

Also, generally, it's speculators and market makers who have an interest in capturing arb opportunities if and when the forward price steps outside no-arb range, not the commercial users who only enter into forwards for business reasons. Is this right? And if it is, then when we use cash and carry to derive the no-arb price, the convenience yield should be irrelavant, hence its only the interest rate cost and storage costs that determine the fair price. Is this right?

Many thanks for your help.

risk taker

coalexander
Posts: 815
Joined: Sun Sep 28, 2008 10:30 pm

Re: No-Arb range of forwards

Postby coalexander » Mon Aug 13, 2012 4:40 pm

Hi,

I guess there is a lower bound given that producers would not choose to produce if the price falls below a certain level. Eg is the price of oil falls below 50$ a barrel many oil fields would not find it economical to produce.

Most of the traders in commodities are large firms like Enron or Glencore (interesting suvery here http://en.wikipedia.org/wiki/Glencore). They look for all inefficiencies in pricing, short-term arbitrages (which are rare anyway) but mainly longer-term speculations, and I guess for spotting pricing inefficiencies they would take all the carry cost including convenience yield into account.

Cheers, Carol

risk taker
Posts: 41
Joined: Wed Aug 10, 2011 12:52 pm

Re: No-Arb range of forwards

Postby risk taker » Wed Aug 15, 2012 11:01 am

Hi Carol,

After some thought, I think that when you say one is limited to one-way arb only for commodities, you really mean those commodities which are consumption assets.

What I really wanted to say in my first post is that when we derive the theoretical forward price for a consumption asset, convenience yield should never enter into the theoretical formula, for the following two reasons. See if my thinking is correct?

1) if the term convenience yield is there in the formula, then it means that one has to estimate the convenience yield. By the nature of this concept, it does not lend itself natually to quantification. I think no one is going to argue that it is not difficult and hard to estimate it, therefore lets drop the task of estimating it entirely, for really how much confidence any forecaster could have in getting an estimate that is reliable! Not much!

2) the second reason is due to that I think what should be in the formula is interest costs and carry costs i.e. the fair price F* equals spot price inflated at interest costs and carry costs. Now this acts as the upper bound of the fair price.
a) If the market price of the forward is greater than F*,then people can conduct cash&carry transactions. But convenience yield should not be taken into account, PRECISELY because arbitrageurs are buying the consumption asset for arbitrage purposes, instead of buying it to realize the convenience yield! In other words, when they do the cash bit of the arb transactions, they are arbitrageurs, not commercial users, so how can convenience yield be relevant to them.
b) if the market price is less than F*, then obviously reverse cash & carry is impossible as one cant go short on a consumption asset. That leaves us with the current owners of the consumption asset to sell it, BUT as we know, the primary participants of the spot consumption asset market are commercial users, therefore they are reluctant to sell it as they plan to use it in some way. So, we end up with a market forward price somewhere less than the upper bound. We can calculate the market impled convenience yield which measures the extent to which the market price is less than the upper bound.

Many thanks again!

risk taker

risk taker
Posts: 41
Joined: Wed Aug 10, 2011 12:52 pm

Re: No-Arb range of forwards

Postby risk taker » Mon Aug 27, 2012 6:54 am

Hi Carol,

could you take a look at my questions please?

Thanks a lot.

risk taker

risk taker
Posts: 41
Joined: Wed Aug 10, 2011 12:52 pm

Re: No-Arb range of forwards

Postby risk taker » Thu Aug 30, 2012 11:20 am

Hi Carol,

My question is whether convenience yield should be there in the fair price formula when we seek to derive a fair price for a commodity forward? Based on my thinking about this issue in my previous rather lenghty post, I think it shouldn't be for those stated reasons there. Do you think it should be there? And why?

Thank you and I benefit hugely from studying your books. And this discussion forum is a real stimulus!!

warm regards, risk taker

coalexander
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Joined: Sun Sep 28, 2008 10:30 pm

Re: No-Arb range of forwards

Postby coalexander » Thu Aug 30, 2012 9:12 pm

Dear Risk-taker,

Carol asked me to look at your post. Considering an underlying which cannot be arbitraged at all may clarify the discussion. Consider a forward contract on temperature at some future date and specific location. You cannot buy or sell this temperature now. What is the fair price (temperature) for the contract to be entered into at par? It may be higher or lower than the current (spot) temperature at the relevant location. It all depends on the forecasts of the market participants (which can be supported by weather forecasting models, etc.). How do we interpret the basis between spot and forward? Does it matter? The spot temperature may be irrelevant in the forecasting model.

The situation is similar for consumable commodities that are difficult (expensive) to store, for example, electricity. One could ask what is the fair forward price of 1 MWh of electricity in London on 23 July 2015 at 5pm? The answer would rely on forecasting models for production and consumption and would probably not be equal to the price now at 9pm on 30/08/12. Would it be useful to interpret the difference between these two prices? Would it matter? Does the spot price matter?

A commodity that is consumable may be needed immediately. The forward price may be much lower than the spot price, but the consumer cannot wait. So it is quite natural to interpret the relatively high spot price by saying that there is a convenience value in having the commodity now. Does it help figure out the fair forward price? Not really. Unless there is a two-way arbitrage between spot and forward prices (storable commodity, not needed for immediate consumption and therefore shortable) the spot prices may not be useful for determining the fair forward price. By the way, the spot price is also irrelevant in any hedging problem.

Jacques Pezier

coalexander
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Re: No-Arb range of forwards

Postby coalexander » Fri Aug 31, 2012 8:56 am

To add to Jacques comment:

I am currently writing a discussion paper, with Annanit Sumnawong and Marcel Propokczuk, which introduces a new three-factor stochastic volatility model for pricing options on consumable commodities. The motivation for this paper came from examining long time series of investable returns* on forwards or futures for consumable commodities, where we found there is no seasonality (except in the volatility). All the seasonality is in the 'convenience yield plus carry cost' terms of the drift, which appears in the non-investable returns* but not in the investable returns. So a model for investable futures (constant maturity or otherwise) on consumable commodities should have neither convenience yield nor carry cost.

* Investable returns are constant-maturity returns linearly interpolated from the returns on the two straddling-maturity traded futures. non-investable returns are onbtained by first linearly interpolating between PRICES of the two straddling-maturity traded futures, gives an indicative price series, but then when we take returns on these prices they are NOT investable -- see Galai (1979) JOF

risk taker
Posts: 41
Joined: Wed Aug 10, 2011 12:52 pm

Re: No-Arb range of forwards

Postby risk taker » Sat Sep 01, 2012 10:40 am

Jacques - thanks so much! It makes sense and i'm clearer now.

Carol - thank you too! I'm ploughing through MRA series and have not reached volatility yet. But when I do, hopefully i can understand your new discussion paper then! Just an aside, the idea of coming up with a MRA certification/designation - is it still on the table??

Cheers, risk taker

coalexander
Posts: 815
Joined: Sun Sep 28, 2008 10:30 pm

Re: No-Arb range of forwards

Postby coalexander » Sat Sep 01, 2012 11:08 am

Yup, the table in the far corner of the room....


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