Fwd: Re: Fundamentals

[Paul Davidson <pdavidson@xxxxxxx>]

> Date: Mon, 26 Mar 2001 10:12:29 -0500
> To: James Juniper <James.Juniper@xxxxxxxxxxxx>
> From: Paul Davidson <pdavidson@xxxxxxx >
> Subject: Re: Fundamentals
>
> At 04:47 PM 3/26/01 +0930, you wrote:
>
> > Since
> > Steve has requested a response I feel obliged to reciprocate. Geometric
> > Browninan motion is the equivalent of a lognormal distribution. The stock
> > grows with a constant drift and a constant volatility. This is far from
> > being a nonergodic process. 
> >
> > More sophisticated models of real option pricing attempt to incorporate
> > stochastic volatility in the underlying asset and stochastic interest
> > rates. This gives rise to an incomplete market problem that can be
> > resolved in a number of ways, requiring that the researcher to specify
> > the exact characteristics of the underlying stochastic process and then
> > apply some method (relative entropy or minimum variance hedging) to
> > select one of the martingale processes from the infinite family of
> > feasible martingale processes that would arise. 
> >
> > However, an alternative to assuming incomplete markets is to price the
> > option under
> > uncertainty
> > aversion
> > after imposing norm
> > bounds over the volatility. This approach
> > can accommodate
> > non-ergodic processes. Some people use fuzzy measure theory (Cherubini, Math. Fin.), other people use capacities or sub-additive probabilities that add up to less than one (Chateauneuf, Math. Finance), and others use multiple-priors where it is assumed that the set of feasible distributions cannot be reduced to a singleton (McEneaney M. of Ops. Res.). 
> >
> > IMHO, the latter approach is closer to what Keynes was talking about and, thus, to what Paul Davidson intends in his rejection of any notion of "the fundamentals". However, without wanting to second-guess his position, I would imagine that Paul would also question the value of all this mathematical formalism anyway.
>
>
> James:  All this math formalism is equivalent to the old ABBA LERNER joke about "The Economists's Can Opener".
>
> Paul