Joshi’s Split Tree for Option Pricing

Guillaume Leduc and Merima Nurkanovic Hot
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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

Risks, 2020, vol. 8, issue 3, 1-26

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.

Keywords: binomial option pricing; error analysis for non-self-similar binomial trees; American options; Black–Scholes (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2020
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