Please use this identifier to cite or link to this item: https://hdl.handle.net/10419/258034 
Year of Publication: 
2020
Citation: 
[Journal:] Risks [ISSN:] 2227-9091 [Volume:] 8 [Issue:] 3 [Article No.:] 81 [Publisher:] MDPI [Place:] Basel [Year:] 2020 [Pages:] 1-26
Publisher: 
MDPI, Basel
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/n3/2 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.
Subjects: 
binomial option pricing
error analysis for non-self-similar binomial trees
American options
Black-Scholes
Persistent Identifier of the first edition: 
Creative Commons License: 
cc-by Logo
Document Type: 
Article
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