Unique Option Pricing Measure with neither Dynamic Hedging nor Complete Markets

Date01 March 2015
Published date01 March 2015
Unique Option Pricing Measure with
neither Dynamic Hedging nor
Complete Markets
Nassim Nicholas Taleb
School of Engineering, NYU, & Former Option Trader
E-mail: nnt1@nyu.edu
Proof that under simple assumptions, such as constraints of PutCall Parity, the
probability measure for the valuation of a European option has the mean derived
from the forward price which can, but does not have to be the riskneutral one,
under any general probability distribution, bypassing the BlackScholesMerton
dynamic hedging argument, and without the requirement of complete markets and
other strong assumptions. We conrm that the heuristics used by traders for
centuries are both more robust, more consistent, and more rigorous than held in the
economics literature. We also show that options can be priced using innite
variance (nite mean) distributions.
Keywords: option theory, derivatives, risk management, hedging
JEL Classification: G13, D81, A14
1. Background
Option valuations methodologies have been used by traders for centuries, in an effective
way (Haug and Taleb, 2010). In addition, valuations by expectation of terminal payoff
forces the mean of the probability distribution used for option prices be be that of the
forward, thanks to PutCall Parity and, should the forward be riskneutrally priced, so will
the option be. The Black Scholes argument (Black and Scholes, 1973; Merton, 1973) is
held to allow riskneutral option pricing thanks to dynamic hedging, as the option
becomes redundant (since its payoff can be built as a linear combination of cash and the
underlying asset dynamically revised through time). This is a puzzle, since: 1) Dynamic
Hedging is not operationally feasible in nancial markets owing to the dominance of
portfolio changes resulting from jumps, 2) The dynamic hedging argument doesnt stand
mathematically under fat tails; it requires a very specicBlack Scholes worldwith many
impossible assumptions, one of which requires nite quadratic variations, 3) Traders use
the same BlackScholes risk neutral argumentfor the valuation of options on assets that
Peter Carr, Marco Avellaneda, Hélyette Geman, Raphael Douady, Gur Huberman, Espen
Haug, and Hossein Kazemi.
European Financial Management, Vol. 21, No. 2, 2015, 228235
doi: 10.1111/eufm.12055
© 2015 John Wiley & Sons Ltd

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