Chapter

Black–Scholes from a Martingale Point of View<sup>*</sup>

Tomas Björk

in Arbitrage Theory in Continuous Time

Second edition

Published in print March 2004 | ISBN: 9780199271269
Published online October 2005 | e-ISBN: 9780191602849 | DOI: http://dx.doi.org/10.1093/0199271267.003.0012

Series: Oxford Finance Series

Black–Scholes from a Martingale Point of View*

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This chapter discusses the standard Black-Scholes model from the martingale point of view. The probability space (Ω, □, P, □-) carrying a P-Wiener process W-, where the filtration □- is the one generated by W-, i.e. □ t = □ t W-. On this space, the model is defined by d S t = α S t D t + σ S t d W- t, d B t = r B t d t. The Black-Scholes model is proven to be arbitrage free and complete.

Keywords: Black-Scholes model; martingale approach; arbitrage; pricing

Chapter.  2447 words. 

Subjects: Financial Markets

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