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From Binomial Model to Black–Scholes Formula

In: Mathematical Financial Economics

Author

Listed:
  • Igor V. Evstigneev

    (University of Manchester)

  • Thorsten Hens

    (University of Zurich)

  • Klaus Reiner Schenk-Hoppé

    (University of Manchester)

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.

Suggested Citation

  • Igor V. Evstigneev & Thorsten Hens & Klaus Reiner Schenk-Hoppé, 2015. "From Binomial Model to Black–Scholes Formula," Springer Texts in Business and Economics, in: Mathematical Financial Economics, edition 127, chapter 15, pages 145-155, Springer.
    • Handle: RePEc:spr:sptchp:978-3-319-16571-4_15
    DOI: 10.1007/978-3-319-16571-4_15
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