Abstract
The binomial pricing model is an option valuation method based on a discrete-time model of the evolution of an equity market. It allows one to determine the fair price of derivatives from the payoff they generate at their expiration date. A formalization of this model in the proof assistant Isabelle is provided. We formalize essential notions in finance such as the no-arbitrage principle and prove that, under the hypotheses of the model, the market is complete, meaning that any European derivative can be replicated by creating a portfolio that generates the same payoff regardless of the evolution of the market.
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- 1.
A short sale consists in borrowing an asset from actor A to sell it to actor B, and then buying the asset at a later point in time to return it to actor A.
- 2.
The subscript in \(V_{n+1}\) is unnecessary, since by definition, derivatives of maturity \(n+1\) are \(\mathcal {F}_{n+1}\)-measurable random variables. It was added to make it easier to keep track of measurability properties of the objects that will be defined.
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Acknowledgments
We thank Hervé Guiol for his valuable comments on this work.
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Echenim, M., Peltier, N. (2017). The Binomial Pricing Model in Finance: A Formalization in Isabelle. In: de Moura, L. (eds) Automated Deduction – CADE 26. CADE 2017. Lecture Notes in Computer Science(), vol 10395. Springer, Cham. https://doi.org/10.1007/978-3-319-63046-5_33
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DOI: https://doi.org/10.1007/978-3-319-63046-5_33
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