What we propose in this book is not a theory; it is a technology. There can be a theory of probability, a theory of Brownian motion, or a theory of valuation of derivatives, but there cannot be a theory of the market of ‘contingent claims’. In our excursion from form into matter, derivatives are renamed contingent claims and their valuation theory is renamed their ‘market’, or their ‘pricing technology’. To repeat, the market of contingent claims is a technology.
Derivative valuation theory, when it is complemented with the crucial process of recalibration, can no longer be a theory; it becomes a technology (i.e. theory + material procedure). Implying volatility from the derivative market price is the first instance of recalibration. It says that BSM should be adopted and simultaneously exceeded.
Another formulation of the recalibration problem is the fundamental principle according to which states of the world in the market are prices, all the prices and nothing but the prices (i.e. they are not abstract states of the world). You cannot couch this principle in a probabilistic theoretical framework.
KeywordsBrownian Motion Formal Register Stochastic Volatility Implied Volatility Contingent Claim
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- 1.Alan W. Richardson, Carnap’s Construction of the World: The Aufbau and the Emergence of Logical Empiricism (Cambridge: Cambridge University Press, 1998).Google Scholar