Black-Scholes without stochastics or PDEs
Abstract
We show how to derive the Black-Scholes model and its generalisation to the `exchange-option' (to exchange one asset for another) via the continuum limit of the Binomial tree. No knowledge of stochastic calculus or partial differential equations is assumed, as we do not use them.
- Publication:
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arXiv e-prints
- Pub Date:
- January 2023
- DOI:
- 10.48550/arXiv.2301.09996
- arXiv:
- arXiv:2301.09996
- Bibcode:
- 2023arXiv230109996M
- Keywords:
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- Quantitative Finance - Pricing of Securities;
- Mathematics - Probability
- E-Print:
- Added S1.7 on derivation of the delta