Is it a coincidence that the binomial tree and Brownian motion should yield a complete market, respectively in discrete time and continuous time? That the market should be complete or incom-plete seems to us so dramatic an alternative, yielding alternative consequences so incommensurate with each other,1 that it cannot depend on picking Brownian motion or the binomial tree among a choice of several available stochastic processes, as if another choice were possible and it was only a coincidence that we had picked Brownian motion or the binomial tree. Brownian motion and the binomial tree seem to us to belong to a category of their own inside which it would no longer be a coincidence if we picked them because they fill it completely — their own special category.
KeywordsBrownian Motion Trading Strategy Stochastic Volatility Implied Volatility Price Process
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