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Risk Neutral Option Pricing With Neither Dynamic Hedging nor Complete Markets

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  • Nassim N. Taleb

Abstract

Proof that under simple assumptions, such as constraints of Put-Call 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 risk-neutral one, under any general probability distribution, bypassing the Black-Scholes-Merton dynamic hedging argument, and without the requirement of complete markets and other strong assumptions. We confirm 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 infinite variance (finite mean) distributions.

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  • Nassim N. Taleb, 2014. "Risk Neutral Option Pricing With Neither Dynamic Hedging nor Complete Markets," Papers 1405.2609, arXiv.org, revised Oct 2014.
    • Handle: RePEc:arx:papers:1405.2609
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    References listed on IDEAS

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    1. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    2. Emanuel Derman & Nassim Nicholas Taleb, 2005. "The illusions of dynamic replication," Quantitative Finance, Taylor & Francis Journals, vol. 5(4), pages 323-326.
    3. Marco Avellaneda & Craig Friedman & Richard Holmes & Dominick Samperi, 1997. "Calibrating volatility surfaces via relative-entropy minimization," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(1), pages 37-64.
    4. Doriana Ruffino & Jonathan Treussard, 2006. "Derman and Taleb's 'The illusions of dynamic replication': a comment," Quantitative Finance, Taylor & Francis Journals, vol. 6(5), pages 365-367.
    5. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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