From Binomial Model to Black–Scholes Formula

Igor V. Evstigneev, Thorsten Hens and Klaus Schenk-Hoppé
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Igor V. Evstigneev: University of Manchester
Thorsten Hens: University of Zurich

Chapter 15 in Mathematical Financial Economics, 2015, pp 145-155 from Springer

Abstract: Abstract The goal of the chapter is to derive the Black-Scholes formula, one of the highlights of Mathematical finance. The proof is conducted by passing to the limit from the binomial model. The chapter begins with introducing some relevant notions: drift and volatility, continuous compounding, geometric random walk, etc. It then shows how to approximate the observed continuous-time price process with constant drift and volatility by price processes generated by suitable binomial models. The main theorem proved in the chapter establishes a general (probabilistic) version of the Black-Scholes formula for a European derivative security with a general payoff function. As a corollary to this theorem, an analytic version of the Black-Scholes formula for a European call option is obtained.

Keywords: Price Process; Nominal Interest Rate; Strike Price; European Call Option; Derivative Security (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sptchp:978-3-319-16571-4_15

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DOI: 10.1007/978-3-319-16571-4_15

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