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Joshi’s Split Tree for Option Pricing

Author

Listed:
  • Guillaume Leduc

    (Department of Mathematics, American University of Sharjah, P.O. Box 26666, Sharjah, UAE)

  • Merima Nurkanovic Hot

    (Department of Mathematics, University of Kaiserslautern, 67653 Kaiserslautern, Germany)

Abstract

In a thorough study of binomial trees, Joshi introduced the split tree as a two-phase binomial tree designed to minimize oscillations, and demonstrated empirically its outstanding performance when applied to pricing American put options. Here we introduce a “flexible” version of Joshi’s tree, and develop the corresponding convergence theory in the European case: we find a closed form formula for the coefficients of 1 / n and 1 / n 3 / 2 in the expansion of the error. Then we define several optimized versions of the tree, and find closed form formulae for the parameters of these optimal variants. In a numerical study, we found that in the American case, an optimized variant of the tree significantly improved the performance of Joshi’s original split tree.

Suggested Citation

  • Guillaume Leduc & Merima Nurkanovic Hot, 2020. "Joshi’s Split Tree for Option Pricing," Risks, MDPI, vol. 8(3), pages 1-26, August.
    • Handle: RePEc:gam:jrisks:v:8:y:2020:i:3:p:81-:d:393079
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    References listed on IDEAS

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