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numbersix


Total Posts: 298
Joined: Jan 2007
 
Posted: 2014-10-14 21:33
But then of course, that you shouldn't like risk-neutral valuation and that I shouldn't like it either but that apparently there should be no escape from it, of course this deep puzzle is a straw man.

BSM is not a model and, because it is not a model, no model can surpass it.

sigma


Total Posts: 105
Joined: Mar 2009
 
Posted: 2014-10-14 21:42
>> But then surely underlying and derivative trade on the same floor, the derivative is triggered by the underlying and nothing else, surely the underlying price follows a stochastic process and surely risk-neutral valuation (or the valuation of the derivative as expectation of payoff under a probability measure that is equivalent to the one under which the underlying process is given) is another name for absence of arbitrage?

We have a slight difference in opinions:
1) I am saying that the underlying stock price is one of key variables (along with stochastic volatility of price returns) for option value&price but atop you have extra variable you need to account for - the stochastic risk premium. The stochastic risk premium has its own source of randomness and can be modeled in a factor-based model (being a factor of some external variables, not specific to price paths of this particular stock )

2) I do not believe in arbitrage-based valuation. Being short skew or vol or credit, you make money almost all the time, but the music does not play all the time and some-times it is very frightening.

3) If the derivative is not replicable, then is has an expected rate-of-return, which is the risk-premium:
a) implied when we speak about prices
b) realized when we speak about the realized P&L
c) equilibrium when we speak about values

numbersix


Total Posts: 298
Joined: Jan 2007
 
Posted: 2014-10-14 21:55
So disbelief in nonarbitrage is your escape route on the territory. I agree with that. However I am interested in the map. Is there arbitrage in your map?

BSM is not a model and, because it is not a model, no model can surpass it.

sigma


Total Posts: 105
Joined: Mar 2009
 
Posted: 2014-10-14 21:56
>> you shouldn't like risk-neutral valuation and that I shouldn't like it either but that apparently there should be no escape from it

why no escape? the risk-neutral valuation is a theoretical concept introduced in late 80-s and early 90-s by academia for publishing papers and getting grants and consultancies. Does the risk-neutral valuation work in the real world?

For this situations, my favorite quote is from Richard P. Feynman: It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong!

numbersix


Total Posts: 298
Joined: Jan 2007
 
Posted: 2014-10-14 22:26
Show me the map, Arthur, the map. I am after a formalism for now and I will worry about the real world later.

BSM is not a model and, because it is not a model, no model can surpass it.

sigma


Total Posts: 105
Joined: Mar 2009
 
Posted: 2014-10-14 22:53
The valuation kernel:
one for option value from seller as function of stock dynamics and risk-premium (spread over implied and realized dynamics)

another for option value from buyer as function of his risk-preference and utility for specific pay-offs.

The option price is the interception of the two kernels.

By the the valuation kernel I mean the integral over the physical distribution of stock-returns and related factors times the state-dependent risk-premium.

Hedging is applied to hedge against changes in physical dynamics. Little point to hedge against changes in the risk-premium - you either take the risk or not.


numbersix


Total Posts: 298
Joined: Jan 2007
 
Posted: 2014-10-15 00:02
And so in your ex-ante map of the territory there is one option seller and one option buyer and no room for an arbitrageur who would make money in case he couldn't find a martingale measure that would explain the options prices and be equivalent to the real one in which the underlying price dynamics are given?

BSM is not a model and, because it is not a model, no model can surpass it.

sigma


Total Posts: 105
Joined: Mar 2009
 
Posted: 2014-10-15 04:07
... arbitrageur, martingale measure, equivalent ...

These are the concepts of the risk-neutral pricing, which we want to get rid of to explain what actually happens in the real world.

By shorting implied vols and credit, you are very likely to make money, but is it an arbitrage or a premium for bearing losses in bad times? Is the premium fairly priced all the times?

numbersix


Total Posts: 298
Joined: Jan 2007
 
Posted: 2014-10-15 04:46
Oh, sure, the real world. So I am supposed to explain the arbitrage that occurs in the real world by a pricing technology (what deeds calls a map) that is itself vulnerable to arbitrage. I doubt any customer would heartily buy into that.

By buying a stock you also make money on average, yet this is not arbitrage either and the stock is rightly priced by the risk-neutral measure.

BSM is not a model and, because it is not a model, no model can surpass it.

sigma


Total Posts: 105
Joined: Mar 2009
 
Posted: 2014-10-15 05:32
Ok. I will leave you to your imaginary world of risk-neutral pricing and arbitrages. Initially I thought the scope was to describe how option prices change in the real world and how to model them there.

numbersix


Total Posts: 298
Joined: Jan 2007
 
Posted: 2014-10-15 05:53
Of course options markets (as opposed to mere risk-neutral valuations) exist in the real world. Everybody knows that and this is why deeds thinks I am after a straw man. However my question and my scope are and have always been whether options markets can exist in the formalism. Apparently everybody thinks the answer is no. I am trying to invent the formalism such that yes. I believe this is a deep problem and that a thought can be revolutionary even if it doesn't consist in inventing the real world.

BSM is not a model and, because it is not a model, no model can surpass it.

numbersix


Total Posts: 298
Joined: Jan 2007
 
Posted: 2014-10-15 06:10
But to be fair, I think what you are really proposing is an alternative formalism of options markets that doesn't make sense of arbitrage activities, right? So in a way you do answer my question.

BSM is not a model and, because it is not a model, no model can surpass it.

sigma


Total Posts: 105
Joined: Mar 2009
 
Posted: 2014-10-15 10:16
If your question is whether we need an alternative formulation (to the risk-neutral pricing) to explain price formation in the markets, then yes. My primary objective is to fit the empirical dynamics of the underlying and its option prices using a stationary model for key factors. I can't see how to do it using the risk-neutral formalism (its key flaw is that derivative securities are redundant and can be perfectly replicated) as in the reality we need to model the supply and demand for options to explain their price formation.

numbersix


Total Posts: 298
Joined: Jan 2007
 
Posted: 2014-10-15 15:12
1) I hope you're not confusing risk-neutral pricing and perfect replication.

2) Granted you have modeled supply and demand in the options market and fitted your factor-model. Am I wrong in assuming the model then predicts the prices of both the underlying and the derivative (the intersection of the buyer's and seller's curve)? And if it does, what is to stop a passerby, who is only looking at the corresponding time processes, from detecting arbitrage opportunities if the option prices do not look as if produced by a pricing kernel? The good thing about statistics is that it screens off the underlying causes and mechanisms. Whatever your favorite model or causal explanation of options supply and demand may be, if it's net result is time series, then somebody will try to fit a pricing kernel to its outputs and will identify arbitrage opportunities if he couldn't. Unless you argued that the price time series resulting from your model ultimately does not fit into the framework of probability altogether (say, it is not stationary or even more radically, as I have been arguing all along, the notion of identifiable states of the world doesn't apply to it), in which case I wonder how you can fit your model to the underlying price dynamics in the first place.

3) Sorry if I seem to insist, but I am against risk-neutral pricing myself and I am only trying to exhaust the case in order to narrow down the criticism on probability and random generators ultimately -- a straw man that seems to show resilience indeed (or maybe just in deeds?).

BSM is not a model and, because it is not a model, no model can surpass it.

Maggette


Total Posts: 922
Joined: Jun 2007
 
Posted: 2014-10-15 15:32
"1) I hope you're not confusing risk-neutral pricing and perfect replication. "

I do confuse them!

Ich kam hierher und sah dich und deine Leute lächeln, und sagte mir: Maggette, scheiss auf den small talk, lass lieber deine Fäuste sprechen...

deeds


Total Posts: 341
Joined: Dec 2008
 
Posted: 2014-10-15 23:40

six

irresistible cleverness, or ad hominem self reference?

To reiterate my position from aeons past - I'm all for the overall program, hungry for something refutable

numbersix


Total Posts: 298
Joined: Jan 2007
 
Posted: 2016-01-19 09:26
Then perhaps you should consider this:

The Medium of Contingency

Newly published, in which the market of contingent claims finally becomes equal to matter.
And matter is redefined.

Is this refutable?

BSM is not a model and, because it is not a model, no model can surpass it.

deeds


Total Posts: 341
Joined: Dec 2008
 
Posted: 2016-01-19 14:58
Thanks, six, I'll have a look...currently on order at my local library

deeds


Total Posts: 341
Joined: Dec 2008
 
Posted: 2016-01-19 14:59
Thanks, six, I'll have a look...currently on order at my local library

numbersix


Total Posts: 298
Joined: Jan 2007
 
Posted: 2016-01-19 15:02
Much obliged.

And impatient.

BSM is not a model and, because it is not a model, no model can surpass it.

numbersix


Total Posts: 298
Joined: Jan 2007
 
Posted: 2016-01-19 15:04
Part of my new speculation is that the time of the underlying price statistics is not identifiable with, and is even incompatible with, the time of the derivative market price.

Probably the reason why, in anticipation, you are posting twice in time.

BSM is not a model and, because it is not a model, no model can surpass it.

numbersix


Total Posts: 298
Joined: Jan 2007
 
Posted: 2016-03-25 20:07
Talk and book launch of The Medium of Contingency.

Enjoy!

Note: In it, dear pj, you will find mention of a book you're familiar with: L'Écriture postérieure.

BSM is not a model and, because it is not a model, no model can surpass it.

pj


Total Posts: 3302
Joined: Jun 2004
 
Posted: 2016-05-07 18:16
A nice explanation.
Alas in Phrench
Although the concept of RBL (Random Bullshit Language) should be clear.

I saw a dead fish on the pavement and thought 'what did you expect? There's no water 'round here stupid, shoulda stayed where it was wet.'

numbersix


Total Posts: 298
Joined: Jan 2007
 
Posted: 2016-05-08 11:19
The only thing more terrifying than Phrench is math.

BSM is not a model and, because it is not a model, no model can surpass it.

Nonius
Founding Member
Nonius Unbound
Total Posts: 12651
Joined: Mar 2004
 
Posted: 2016-05-08 16:13
and the guy was doing "economics". Now if he were scribbling algebra, I might understand.

Chiral is Tyler Durden
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