
But then of course, that you shouldn't like riskneutral 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 


>> 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 riskneutral 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 factorbased model (being a factor of some external variables, not specific to price paths of this particular stock )
2) I do not believe in arbitragebased 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 sometimes it is very frightening.
3) If the derivative is not replicable, then is has an expected rateofreturn, which is the riskpremium: a) implied when we speak about prices b) realized when we speak about the realized P&L c) equilibrium when we speak about values





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 


>> you shouldn't like riskneutral valuation and that I shouldn't like it either but that apparently there should be no escape from it
why no escape? the riskneutral valuation is a theoretical concept introduced in late 80s and early 90s by academia for publishing papers and getting grants and consultancies. Does the riskneutral 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! 




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 


The valuation kernel: one for option value from seller as function of stock dynamics and riskpremium (spread over implied and realized dynamics)
another for option value from buyer as function of his riskpreference and utility for specific payoffs.
The option price is the interception of the two kernels.
By the the valuation kernel I mean the integral over the physical distribution of stockreturns and related factors times the statedependent riskpremium.
Hedging is applied to hedge against changes in physical dynamics. Little point to hedge against changes in the riskpremium  you either take the risk or not.





And so in your exante 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 


... arbitrageur, martingale measure, equivalent ...
These are the concepts of the riskneutral 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?





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 riskneutral 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 


Ok. I will leave you to your imaginary world of riskneutral 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. 




Of course options markets (as opposed to mere riskneutral 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. 




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 


If your question is whether we need an alternative formulation (to the riskneutral 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 riskneutral 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. 





1) I hope you're not confusing riskneutral pricing and perfect replication.
2) Granted you have modeled supply and demand in the options market and fitted your factormodel. 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 riskneutral 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: 929 
Joined: Jun 2007 


"1) I hope you're not confusing riskneutral 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 


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 




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 


Thanks, six, I'll have a look...currently on order at my local library 



deeds


Total Posts: 341 
Joined: Dec 2008 


Thanks, six, I'll have a look...currently on order at my local library 





Much obliged.
And impatient. 
BSM is not a model and, because it is not a model, no model can surpass it. 



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. 




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: 3305 
Joined: Jun 2004 


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.'





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: 12657 
Joined: Mar 2004 


and the guy was doing "economics". Now if he were scribbling algebra, I might understand. 
Chiral is Tyler Durden 


