Chapter 43. Black-Scholes Option Pricing Model

SVETLOZAR T. RACHEV, PhD, DrSci

Chair-Professor, Chair of Econometrics, Statistics and Mathematical Finance, School of Economics and Business Engineering, University of Karlsruhe and Department of Statistics and Applied Probability, University of California, Santa Barbara

CHRISTIAN MENN, Dr. rer. pol.

Associate, Sal. Oppenheim Jr. & Cie, Frankfurt, Germany

FRANK J. FABOZZI, PhD, CFA, CPA

Professor in the Practice of Finance, Yale School of Management

Abstract: The most popular continuous-time model for option valuation is based on the Black-Scholes theory. Although certain drawbacks and pitfalls of the Black-Scholes option pricing model have been understood shortly after its publication in the early 1970s, it is still by far the most popular model for option valuation. The Black-Scholes model is based on the assumption that the underlying follows a stochastic process called geometric Brownian motion. Besides pricing, every option pricing model can be used to calculate sensitivity measures describing the influence of a change in the underlying risk factors on the option price. These risk measures are called the "Greeks" and their use will be explained and described.

Keywords: Black-Scholes option pricing model, option valuation, Greeks, geometric Brownian motion, put-call parity

In this chapter, we look at the most popular model for pricing options, the Black-Scholes model, and look at the assumptions and their importance. We also explain the ...

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