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TCO
15-03-2008, 17:47:32
If we take the futures price of a commodity as sort of the market's "50 case" for what it thinks a commodity will cost in the future, is there a calculation one can make or an instrument that one can buy that will give the "10" and "90" cases?

KrazyHorse
15-03-2008, 18:19:47
a) futures prices are not what the market thinks there is a 50% chance of the price being. They are the expectation value (mod some degree of risk premium). In other words, if there's a 30% chance that oil will be 100 in 6 months, a 40% chance that it will be 110 and a 30% chance it will be 500 then the 6 month futures price will NOT be 110 (the median of the distribution). It will be 224 (0.3*100+0.4*110+0.3*500)

b) Options prices give you the future probability of any commodity price. Especially "European options". American options are redeemable at any time before expiry, while Euro ones are only redeemable at the expiry only. American options are therefore slightly more complicated. To see how to get the probabilities out of option prices, then say oil is at 110$/bbl currently. The cost to buy a Euro call option (giving you the option to buy oil) on 1000 bbl expiring in 6 months with a strike price of 150$/bbl is 10000$. This means that the market expectation of:

Int(from price = 150 to infinity) P(price) * (price-150$/bbl) dprice = 10000$/1000bbl = 10$/bbl

Where price is the price in 6 months and P(price) is the normalised probability dist. of that price.

Now, lets say that you can buy the exact same option with a strike price of 151$/bbl for 9900$

Int(from price = 151 to infinity) P(price) * (price-151$/bbl) dprice = 9900$/1000bbl = 9.9$/bbl

Now, as long as you've picked two strike prices which are very near each other (150$/bbl and 151$/bbl) and as long as the probability dist. is not strongly peaked from 150$/bbl-151$/bbl then the difference is option prices is approximately

(optionprice(150$/bbl) - optionprice(151$/bbl))/1000bbl = 0.1$/bbl =

Integral(price=150$/bbl to infinity) P(price) * (151$/bbl - 150$/bbl) dprice =

Integral(price=150$/bbl to infinity) P(price) * (1$/bbl) dprice


So Integral(price=150$/bbl to infinity) P(price) dprice = 0.1

So the probability of oil being higher than 150$ in 6 months is 0.1

KrazyHorse
15-03-2008, 18:21:24
Note that the above does not take into account the fact that you need to discount the value of options and futures prices with both risk premia AND a risk-free rate of return (say 4-5% p.a.). You pay the price on the option NOW and hope to collect LATER

KrazyHorse
15-03-2008, 18:25:42
To formalize my above example, if the price per unit for a Euro call option at strike price P1 is Q1 for term T and the price per unit for a Euro call option at strike price P2 is Q2 for the same term then assuming P(price between P1 and P2) << 1 the probability of the price being higher than P1 after term T is (Q1-Q2)/(P2-P1)

KrazyHorse
15-03-2008, 18:28:14
Or, if you have a continuous option price distribution (instead of option prices at discrete intervals) then P(price greater than strike price) = -d(call option price)/d(strike price)

KrazyHorse
15-03-2008, 18:30:15
If you want to use option prices which have large differences in strike price, or different expiry dates than things get more complicated.

Vincent
15-03-2008, 18:34:22
Wow, this is even MORE exciting.

KrazyHorse
15-03-2008, 18:34:49
Thank you.

Vincent
15-03-2008, 18:35:52
I pissed in my pants!!!

KrazyHorse
15-03-2008, 18:37:12
I CAME IN MINE

Vincent
15-03-2008, 18:38:52
Smells good

KrazyHorse
15-03-2008, 18:41:33
nm

TCO
15-03-2008, 19:47:40
So can you give me the 10, 50 and 90 cases for the price of oil 5 years from now, based on market view?

mr_B
15-03-2008, 19:50:07
beeeee baaaaaaa borrrrrrrrrrrrrrrrrrrrrrrrrrring

KrazyHorse
15-03-2008, 20:41:09
Originally posted by TCO
So can you give me the 10, 50 and 90 cases for the price of oil 5 years from now, based on market view?

Oil doesn't trade in 5 year futures, or options.

IIRC you can go 6 months out at most.

EDIT: nm, I might be wrong on that 6 month horizon thing.

But AFAIK the market in 5 year oil options is going to be pretty shallow. It'll be hard to come up with a meaningful number.

KrazyHorse
15-03-2008, 20:48:12
If you can give me European option prices for different strike prices settling 5 years out then I can give you those numbers.

KrazyHorse
15-03-2008, 20:49:01
Originally posted by TCO
So can you give me the 10, 50 and 90 cases for the price of oil 5 years from now, based on market view?

Stop being so lazy. Read what I wrote. It's a simple application of the fundamental theorem of calculus.

Vincent
15-03-2008, 22:18:42
Originally posted by mr_B
beeeee baaaaaaa borrrrrrrrrrrrrrrrrrrrrrrrrrring

mr_B
15-03-2008, 22:24:41
badda bing

TCO
15-03-2008, 22:29:17
That sounds like a good approach Kitty. I can't find those different options on the net. Maybe I need to have a finance person pull this out of some database or something.

Vincent
15-03-2008, 22:45:47
Originally posted by mr_B
badda bing

mr_B
15-03-2008, 22:56:30
Originally posted by Vincent

zmama
15-03-2008, 23:23:39
oh kewl

Shining1
16-03-2008, 04:47:37
ECON FORUM!