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ppauper
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Price option where underlying has cap and a floor

January 29th, 2014, 6:28 pm

QuoteOriginally posted by: jonokrugerI don't see why someone would sell in the forward market below the spot floor price. I suppose there is nothing stopping them (maybe for a hedging reason where they can't sell in the spot market)QuoteThe Commission of the European Communities (CEC & 2008 6) described backwardation and contango in relation to futures prices: "The futures price may be either higher or lower than the spot price. When the spot price is higher than the futures price, the market is said to be in backwardation. It is often called "normal backwardation" as the futures buyer is rewarded for risk he takes off the producer. If the spot price is lower than the futures price, the market is in contango."(CEC & 2008 6)
 
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Alan
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Price option where underlying has cap and a floor

January 29th, 2014, 9:55 pm

QuoteOriginally posted by: jonokrugerYes there would be a cost to store the natural gas.They can just say no if they don't want to sell at that level.I think the reason you're not getting an answer to your original question is that thewhole cap and floor business is just too ill-defined and getting the details of it islike pulling teeth. If a term sheet or prospectus exists for these putative options, perhapsyou should post that. Also, post a link or two that fully describes this spot natural gas market withthe trading rules. Without that kind of info, I will guess this discussion is going nowhere..
 
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jonokruger
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Price option where underlying has cap and a floor

January 30th, 2014, 9:22 am

Point taken on the backwardation.I'll get some more comprehensive details to post. Sorry for the frustration.
Last edited by jonokruger on January 29th, 2014, 11:00 pm, edited 1 time in total.
 
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MHill
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Price option where underlying has cap and a floor

January 30th, 2014, 8:16 pm

My (usually simplistic and badly explained) view of Black Scholes:Black Scholes is based on drawing a lognormal probability distribution (probability on y-axis, price on x-axis). The arithmetic mean of the distribution is equal to the forward price of the asset (risk neutral assumption). You then draw a vertical line at the strike price. Calculate area under the curve above the strike price, then discount to present value to get a call option price. That is, you're calculating the sum of all probability weighted possible payoffs. Calculate the area under the curve below the strike price and discount to get a put option price.Black Scholes assumes continuous pricing, and so uses integration to calculate the area under the curve.How this applies to your problem:You could draw your own curtailed (is that the right word?) distribution, possibly with big spikes where the cap and floor are. Find a way to integrate (good luck with that), and go from there.Alternately you could go with discrete pricing, and assign each price a probability, and sum probability * price to get the area, and go from there.Remember to ensure the arithmetic mean of your distribution equals the forward price.As a separate issue, (in case you didn't pick this up) it seems to me that daveangel is saying that, in a market without caps and floors, you might be able to model gas as being lognormal. Call this free-market gas just now. With a regulatory cap, then owning the gas is like being long free-market gas, but short a call option with strike price = cap. No matter how high the free-market price goes, you can never get more than the cap/strike. Similarly, the floor makes you long a put with strike = floor.So looking at it this way, natural gas is a portfolio of free-market gas, a put, and a short call.The question you originally asked then becomes a question of how to value an option on this portfolio using a closed form solution. Sorry I've no actual answers. I hope this helps clarify, and gives you ideas.
Last edited by MHill on January 29th, 2014, 11:00 pm, edited 1 time in total.
 
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MHill
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Price option where underlying has cap and a floor

January 30th, 2014, 8:59 pm

So (given my earlier rambling) could you model a call option on natural gas as a portfolio of:call on 'free-market' gas with strike = actual strikeShort call on free-market gas with strike = capLong a digital call on free-market gas with strike = cap?Then you just need to model free-market gas as a lognormal distribution around the forward price (assuming that's valid for the gas market)You'd have a similar portfolio to replicate the put option
Last edited by MHill on January 29th, 2014, 11:00 pm, edited 1 time in total.
 
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jonokruger
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Price option where underlying has cap and a floor

January 30th, 2014, 9:08 pm

MHill thanks for the input and ideas.I like you suggestion of your curtailed distribution approach using discrete pricing. My thinking is to use past data to create the distribution and then price the option off of that (discounting the area under the curve). I have my doubts whether a closed form solution can be found because of not being able to integrate. Unless I find the data resembles some other distribution (not lognormal) which can be integrated?I'll look into the 'free-market' gas with calls/puts at the caps/floors. I will investigate as to whether the gas market does follow a lognormal distribution if it is unconstrained.Thanks
 
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MHill
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Price option where underlying has cap and a floor

January 31st, 2014, 5:50 am

QuoteOriginally posted by: MHillThen you just need to model free-market gas as a lognormal distribution around the forward price (assuming that's valid for the gas market)Mmm. Not quite right. The forward price needs to be the weighted average of the distribution of the free-market plus the options.Am also having doubt about throwing in digital options. The idea there was to capture the fact you'd get paid cap - strike for all probabilities of free market being greater than cap. It needs quite a bit more thought, but I think it could be promising.Anyway, good luck with it!
 
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spacemonkey
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Price option where underlying has cap and a floor

February 1st, 2014, 12:27 am

QuoteOriginally posted by: jonokrugerHi AlanThanks for the interest.Yes they are. It's a case where there is a floor at which you can buy the underlying (electricity or gas) in the spot market. So no one would sell a forward at below the spot floor because they would be selling below what they can buy in the spot market (arbitrage argument like you mentioned).In terms of option pricing it's the opposite of "fat tails" problem because the probability of the underlying going below the floor is zero. I would call it "thin tails". The normal distribution assumes a probability of the underlying trading below floor which is the problem.Any ideas?Sorry I don't have a chart at this stage.I entered into some correspondence with a great friend of mine. I am baffled by his reply, however it may be of some use to you:"From beyond the darkest mountains; from beneath the cold, heartless ocean; for countless aeons their wicked imaginings had conjured such evils that would strike any mortal man with an incurable madness. A madness which I feel enveloping me, even as I write this.They had imagined a market, yes with a liquidly traded underlying asset, who's price S(t) was modelled by a geometric Brownian motion like other markets - it is true - but no mere Black-Scholes model this. For this carried a terrible curse, a curse beyond measure, real world or risk-neutral, and had been damned for all eternity - trapped behind an impenetrable upper-bound, at a level we know only as B. They cared not for an absence of arbitrage, or uniqueness of prices, their cold minds capable of reckoning tortures beyond the possibilities of logic, beyond even the logic of possibilities. They cared not for liquidity, knowing the shame and suffering that this has wrought upon both man and beast. They cared not for interest rates, which they set to zero, for they are boring.I heard them, in the distance, as I still hear them now. Cackling, wailing, howling. I should have turned back, but I was a fool. I pressed on, even as they summoned up a great call option from the inferno itself, with a pay-off (S(T) - K)^+ at the time of tribulation, T.And I knew that I was not to be spared, my downfall at my own hand, because I knew, yes, yes, I would replicate that payoff using the available assets. For, I could not stop myself, the temptation was too great. My fate was sealed.I stepped forth and took their offering, a trading strategy, worth (S(T) - K)^+ at T, but also worth (B - K)^+ whenever S(t) should approach its greatest upper limit. An unusual strategy, perhaps, but not unknown in the museums and great schools of mankind. The kind of strategy that could sit unnoticed, gathering dust, an unloved exhibit in a storeroom of barrier options.Oh, but this was an abomination. A twisted wretch, a deformed misery, a strategy unlike other barrier options. Should S(t) never approach the limits of it's containment, then, it would simply reproduce the payoff at maturity as all other replicating strategies do But this strategy would not, could not be stopped until the very end of contract itself.Should S(t) merely touch B, before the time of tribulation, T, then the eternal reward (B-K)^+, would be equal to the option reward. Thus endowed I would await the arrival of the tribulation. Should it fail to arrive, should S(t) retreat from B, I would use my reward to give rebirth to the strategy, and this endless, ceaseless cycle I must repeat over and over and over until..."And there it ends. Whatever has happened in the years since I saw him last, it seems he has gone quite mad. Sorry I couldn't answer your question.
 
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investor82
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Price option where underlying has cap and a floor

February 20th, 2014, 8:04 pm

Here's a writeup I did that could help assuming there is an upper barrier https://en.wikipedia.org/wiki/User:Barr ... sandboxthe problem is such options may not obey put call parity
Last edited by investor82 on February 19th, 2014, 11:00 pm, edited 1 time in total.