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.