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On the Minimal Entropy Martingale Measure and Multinomial Lattices with Cumulants

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  • Cyrus Seera Ssebugenyi
  • Ivivi Joseph Mwaniki
  • Virginie S. Konlack

Abstract

In this article, we describe with relevant examples based on empirical data how to use the minimal entropy martingale measure (MEMM) to price European and American Options in multinomial lattices which take into account cumulants information. For trinomial lattices, we show that minimal entropy prices are close to results obtained using the Black and Scholes option pricing formula. For pentanomial lattices, minimal entropy prices are close to results obtained under the mean-correcting martingale measure using the discrete Fourier transform. The MEMM is very easy to compute and is therefore a good candidate for option pricing in multinomial lattices.

Suggested Citation

  • Cyrus Seera Ssebugenyi & Ivivi Joseph Mwaniki & Virginie S. Konlack, 2013. "On the Minimal Entropy Martingale Measure and Multinomial Lattices with Cumulants," Applied Mathematical Finance, Taylor & Francis Journals, vol. 20(4), pages 359-379, September.
    • Handle: RePEc:taf:apmtfi:v:20:y:2013:i:4:p:359-379
    DOI: 10.1080/1350486X.2012.714226
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    Cited by:

    1. Ivivi J. Mwaniki, 2017. "On skewed, leptokurtic returns and pentanomial lattice option valuation via minimal entropy martingale measure," Cogent Economics & Finance, Taylor & Francis Journals, vol. 5(1), pages 1358894-135, January.
    2. Roberto Fontana & Patrizia Semeraro, 2023. "Measuring distribution risk in discrete models," Papers 2302.08838, arXiv.org.

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