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

Author

Listed:
  • Qiang Liu

    (School of Management, University of Electronic Science & Technology of China)

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.

Suggested Citation

  • Qiang Liu, 2005. "Options Pricing with Arithmetic Brownian Motion and its Implication for Risk-Neutral Valuation," Finance 0512001, EconWPA.
  • Handle: RePEc:wpa:wuwpfi:0512001
    Note: Type of Document - pdf; pages: 5
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    File URL: https://econwpa.ub.uni-muenchen.de/econ-wp/fin/papers/0512/0512001.pdf
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    More about this item

    Keywords

    risk-neutral valuation; arithmetic Brownian motion; options price formula;

    JEL classification:

    • G - Financial Economics

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