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- Title
HERMITE BINOMIAL TREES: A NOVEL TECHNIQUE FOR DERIVATIVES PRICING.
- Authors
LECCADITO, ARTURO; TOSCANO, PIETRO; TUNARU, RADU S.
- Abstract
Edgeworth binomial trees were applied to price contingent claims when the underlying return distribution is skewed and leptokurtic, but with the limitation of working only for a limited set of skewness and kurtosis values. Recently, Johnson binomial trees were introduced to accommodate any skewness-kurtosis pair, but with the drawback of numerical convergence issues in some cases. Both techniques may suffer from non-exact matching of the moments of distribution of returns. A solution to this limitation is proposed here based on a new technique employing Hermite polynomials to match exactly the required moments. Several numerical examples illustrate the superior performance of the Hermite polynomials technique to price European and American options in the context of jump-diffusion and stochastic volatility frameworks and options with underlying asset given by the sum of two lognormally distributed random variables.
- Subjects
PRICING; BINOMIAL theorem; TREE graphs; DISTRIBUTION (Economic theory); VALUE (Economics); RATE of return; HERMITE polynomials; OPTIONS (Finance)
- Publication
International Journal of Theoretical & Applied Finance, 2012, Vol 15, Issue 8, p-1
- ISSN
0219-0249
- Publication type
Article
- DOI
10.1142/S0219024912500586