Options Pricing with Arithmetic Brownian Motion and its Implication for Risk-Neutral Valuation

Qiang Liu
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Qiang Liu: School of Management, University of Electronic Science & Technology of China

Finance from University Library of Munich, Germany

Abstract: Risk-neutral valuation is used widely in derivatives pricing. It is shown in this paper, however, that the naïve approach of simply setting the growth rate of the underlying security to risk-free interest rate, which happens to work for a geometric Brownian motion (GBM) process, fails to work when the underlying price follows the arithmetic Brownian motion (ABM). Therefore, the formal approach using a martingale measure should be used instead when the underlying process is not a GBM.

Keywords: risk-neutral valuation; arithmetic Brownian motion; options price formula (search for similar items in EconPapers)
JEL-codes: G (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-fmk and nep-sea
Date: 2005-12-01
Note: Type of Document - pdf; pages: 5
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Persistent link: https://EconPapers.repec.org/RePEc:wpa:wuwpfi:0512001

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