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Lattice Approach and Implied Trees

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Handbook of Computational Finance

Part of the book series: Springer Handbooks of Computational Statistics ((SHCS))

Abstract

Lattice methods or tree methods have become standard tools for pricing many types of options, since they are robust and easy to implement. The basic method is built on a binomial tree and assumes constant volatility and constant relative node spacing. The tree grows from the initial spot price, until maturity is reached. There the payoff is evaluated, and a subsequent backward recursion yields the value of the option. The resulting discrete-time approach is consistent with the continuous Black-Scholes model. This basic lattice approach has been extended to cope with a variable local volatility. Here the lattice nodes are determined based on market data of European-style options. In this way an “implied tree” is created matching the volatility smile. This chapter introduces into tree methods.

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Authors and Affiliations

  1. Mathematisches Institut der Universität zu Köln, Weyertal 86, 50931, Köln, Germany

    Rüdiger U. Seydel

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  1. Rüdiger U. Seydel
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Correspondence to Rüdiger U. Seydel .

Editor information

Editors and Affiliations

  1. , Risk Management Institute, National University of Singapore, 21 Heng Mui Keng Terrace, Level 4, Singapore, 119613, Singapore

    Jin-Chuan Duan

  2. L.v.Bortkiewicz Chair of Statistics, C.A.S.E. Centre f. Appl. Stat. & Econ., Humboldt-Universität zu Berlin, Unter den Linden 6, Berlin, 10099, Germany

    Wolfgang Karl Härdle

  3. , Department of Computational and Data Sci, George Mason University, University Drive 4400, Fairfax, 22030, Virginia, USA

    James E. Gentle

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Seydel, R.U. (2012). Lattice Approach and Implied Trees. In: Duan, JC., Härdle, W., Gentle, J. (eds) Handbook of Computational Finance. Springer Handbooks of Computational Statistics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17254-0_20

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