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Formalizing the Cox-Ross-Rubinstein pricing of European derivatives in Isabelle/HOL

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  • Mnacho Echenim
  • Herv'e Guiol
  • Nicolas Peltier

Abstract

We formalize in the proof assistant Isabelle essential basic notions and results in financial mathematics. We provide generic formal definitions of concepts such as markets, portfolios, derivative products, arbitrages or fair prices, and we show that, under the usual no-arbitrage condition, the existence of a replicating portfolio for a derivative implies that the latter admits a unique fair price. Then, we provide a formalization of the Cox-Rubinstein model and we show that the market is complete in this model, i.e., that every derivative product admits a replicating portfolio. This entails that in this model, every derivative product admits a unique fair price.

Suggested Citation

  • Mnacho Echenim & Herv'e Guiol & Nicolas Peltier, 2018. "Formalizing the Cox-Ross-Rubinstein pricing of European derivatives in Isabelle/HOL," Papers 1807.09873, arXiv.org, revised Aug 2018.
    • Handle: RePEc:arx:papers:1807.09873
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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. 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.
    3. Cox, John C. & Ross, Stephen A. & Rubinstein, Mark, 1979. "Option pricing: A simplified approach," Journal of Financial Economics, Elsevier, vol. 7(3), pages 229-263, September.
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