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A simple proof of the martingale property in a semi-log-normal stochastic volatility model

Volume 45 / 2018

Jacek Jakubowski, Maciej Wiśniewolski Applicationes Mathematicae 45 (2018), 1-4 MSC: 91B25, 60H30, 91G80. DOI: 10.4064/am2356-11-2017 Published online: 5 February 2018

Abstract

A simple proof of a martingale property of the price process in a semi-log-normal stochastic volatility model is presented. The proof is based on the Girsanov theorem and some elementary properties of functionals of Brownian motion.

Authors

  • Jacek JakubowskiInstitute of Mathematics
    University of Warsaw
    02-097 Warszawa, Poland
    e-mail
  • Maciej WiśniewolskiInstitute of Mathematics
    University of Warsaw
    02-097 Warszawa, Poland
    e-mail

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