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Derivatives and the Wealth of Societies$
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Benjamin Lee and Randy Martin

Print publication date: 2016

Print ISBN-13: 9780226392660

Published to Chicago Scholarship Online: May 2017

DOI: 10.7208/chicago/9780226392974.001.0001

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PRINTED FROM CHICAGO SCHOLARSHIP ONLINE (www.chicago.universitypressscholarship.com). (c) Copyright University of Chicago Press, 2022. All Rights Reserved. An individual user may print out a PDF of a single chapter of a monograph in CHSO for personal use.date: 26 June 2022

On Black-Scholes1

On Black-Scholes1

(p.240) Chapter Seven On Black-Scholes1
Derivatives and the Wealth of Societies

Elie Ayache

University of Chicago Press

This chapter draws upon the author's experience as a trader and designer of options software. His first day of trading was Black Monday, when global stock markets crashed >20%. At that time, Black-Scholes was the standard model used to price options; his experience on Black Monday made him suspicious of the traditional understanding of probability and possibility. Using the ideas of Meillassoux, Ayache argues that “the event is unrepresentable”; yet what options pricing models presuppose is instantaneous volatility that sets market prices in the act of trading. All models must fail as explanatory devices, yet Ayache insists that their failure makes it possible for options to be traded, otherwise there would be no need for a market. For Ayache, value “doesn’t exist” because values are model-dependent; prices are given by the market; the price of a financial asset is given by its instantaneous volatility in the act of trading. The development of implied volatility, calculated from the market price of the option inserted into an “inverted” Black-Scholes equation to calculate the volatility of the underlying stock, is the closest derivative finance gets to the event of trading but it remains the model’s estimate of the future volatility of the stock.

Keywords:   Black-Scholes, Brownian motion, redundancy, stochastic volatility, recalibration, regime switching, jump diffusion, market maker, value, liquidity

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