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Many problems in valuing complex derivatives are solved by using discrete multinomial approximations. In this article, we suggest two modifications for Kamrad and Ritchken (1991) multinomial approximating model. First, we propose the inclusion of an omitted second order term to reduce errors. Second, we ensure non-negative probabilities by bounding the stretch parameter, which parameterizes the size of the up-and down-jumps in the lattice. From a standpoint of assessing the computational effort, we derive mathematical expressions to determine the number of nodes generated by the approximation process for a k asset model. Numerical examples are presented to illustrate gain in accuracy of the proposed model on pricing options and computational efficiency.

References


Boyle, P. P.(1988).A lattice framework for option pricing with two state variables.Journal of Financial and Quantitative Analysis.23(1),1-12.
Boyle, P. P.,Evnine, J,Gibbs, S.(1989).Numerical evaluation of multivariate contingent claims.The Review of Financial Studies.2(2),241-250.
Johnson, H.(1987).Options on the maximum or the minimum of several assets.Journal of Financial and Quantitative Analysis.22(3),277-283.
Kamrad, B.,Ritchken, P.(1991).Multinomial approximating model for options with k-state variables.Management Science.37(12),1640-1652.
Miller, I.,Miller, M.(1999).John E. Freund's mathematical statistics.New Jersey:Prentice Hall.

Cited by


陳慶全(2006)。改良型環狀類神經網路架構之實現與應用〔碩士論文,國立臺北科技大學〕。華藝線上圖書館。https://www.airitilibrary.com/Article/Detail?DocID=U0006-2607200614545200

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