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Numerical Approximation of the Implied Volatility Under Arithmetic Brownian Motion


  • Jaehyuk Choi
  • Kwangmoon Kim
  • Minsuk Kwak


We provide an accurate approximation method for inverting an option price to the implied volatility under arithmetic Brownian motion, which is widely quoted in Fixed Income markets. The maximum error in the volatility is in the order of 10-10 of the given option price and much smaller for the near-the-money options. Thus our approximation can be used as an exact solution without further refinements of iterative methods.

Suggested Citation

  • Jaehyuk Choi & Kwangmoon Kim & Minsuk Kwak, 2009. "Numerical Approximation of the Implied Volatility Under Arithmetic Brownian Motion," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(3), pages 261-268.
  • Handle: RePEc:taf:apmtfi:v:16:y:2009:i:3:p:261-268
    DOI: 10.1080/13504860802583436

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    1. repec:bla:jfnres:v:40:y:2017:i:3:p:401-427 is not listed on IDEAS
    2. Cyril Grunspan, 2011. "A Note on the Equivalence between the Normal and the Lognormal Implied Volatility : A Model Free Approach," Papers 1112.1782,


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