American Journal of Applied Mathematics

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An Adjusted Trinomial Lattice for Pricing Arithmetic Average Based Asian Option

Received: 09 November 2017    Accepted: 22 November 2017    Published: 24 March 2018
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Abstract

An adjusted trinomial model for pricing both European and American arithmetic average-based Asian options is proposed. The Kamrad and Ritchken trinomial tree governs the underlying asset evolution. The algorithm selects a subset of the true averages realized at each node to serve as the representative averages. The option prices are then computed via backward induction and interpolation. The results show that the trinomial method produces more accurate prices especially in the case of European style Asian options.

DOI 10.11648/j.ajam.20180602.11
Published in American Journal of Applied Mathematics (Volume 6, Issue 2, April 2018)
Page(s) 28-33
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Asian Options, Arithmetic Average, Lattice, Trinomial

References
[1] Zhang, P. G. Exotic Options: A guide to second generation options. s. l.: World Scientific, 1998.
[2] Pricing European Average rate currency options. Levy, E. 1992, International Money and Finance, Vol. 11, pp. 474-491.
[3] Prices and Hedge ratios of Average rate exchange options. Vorst, T. 1992, International Review of Financial analysis, Vol. 1, pp. 179-193.
[4] A quickalgorithm for pricing European average options. S. M. Turnbull, L. M. Wakeman. 3, 1991, Journal of Financial and Quantitative Analysis377-389, Vol. 26.
[5] P. Wilmott, J. Dewynne, S. Howison. Option Pricing: MAthematical Models and Computation. Oxford: Oxford Financial Press, 1993.
[6] A new PDE approach for pricing arithmetic average Asian options. Vecer, J. 4, Journal of Computational Finance, Vol. 4, pp. 105-113.
[7] Efficient Procedures for valuing European and American path-dependent options. J. Hull, A. White. 1993, Journal of Derivatives, Vol. 1, pp. 21-31.
[8] Option pricing: A simplified Approach. J. C. Cox, S. A. Ross, M. Rubinstein. 1979, Journal of Financial Economics, Vol. 7, pp. 229-264.
[9] Convergence of Numerical Methods for Valuing Path Dependent Options using Interpolation. P. A. Forsyth, K. R. Vetzal and R. Zvan. 2002, Rev Derivatives, Vol. 5.
[10] An adfjusted binomial model for pricing Asian options. M. Costabile, E. Russo and I. Massabo. 2006, Rev Quant Finance, Vol. 27, pp. 285-296.
[11] Robust Numerical PDE models for Asian Options. R. Zvan, P. A. Forsyth and K. R. Petal. 2, 1998, Journal of Computational Finance, Vol. 1, pp. 39-78.
[12] Simple, Fast and Flexible pricing of Asian options. Klaasen, T. R. 3, 2001, Vol. 4, pp. 89-124.
[13] Pricing Asian options with Lattices. Dai, T. S. s. l.: Department of Computer Science and Information Engineering, National Taiwan University, 2004, Ph.D. Thesis.
[14] Option valuation using a three-jump process. Boyle, P. 7-12, 1986, International Options Journal, Vol. 3.
[15] Multinomial approximating models for options with k state variables. Ritchken, B. Kamrad and P. 1991, Management Science, Vol. 37, pp. 1640-1652.
Author Information
  • Mathematics, Pan African University Institute for Basic Sciences, Technology and Innovation, Nairobi, Kenya

  • Mathematics, Pan African University Institute for Basic Sciences, Technology and Innovation, Nairobi, Kenya

  • Mathematics, Pan African University Institute for Basic Sciences, Technology and Innovation, Nairobi, Kenya

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  • APA Style

    Dennis Odhiambo Ogot, Phillip Ngare, Joseph Mung’atu. (2018). An Adjusted Trinomial Lattice for Pricing Arithmetic Average Based Asian Option. American Journal of Applied Mathematics, 6(2), 28-33. https://doi.org/10.11648/j.ajam.20180602.11

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    ACS Style

    Dennis Odhiambo Ogot; Phillip Ngare; Joseph Mung’atu. An Adjusted Trinomial Lattice for Pricing Arithmetic Average Based Asian Option. Am. J. Appl. Math. 2018, 6(2), 28-33. doi: 10.11648/j.ajam.20180602.11

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    AMA Style

    Dennis Odhiambo Ogot, Phillip Ngare, Joseph Mung’atu. An Adjusted Trinomial Lattice for Pricing Arithmetic Average Based Asian Option. Am J Appl Math. 2018;6(2):28-33. doi: 10.11648/j.ajam.20180602.11

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  • @article{10.11648/j.ajam.20180602.11,
      author = {Dennis Odhiambo Ogot and Phillip Ngare and Joseph Mung’atu},
      title = {An Adjusted Trinomial Lattice for Pricing Arithmetic Average Based Asian Option},
      journal = {American Journal of Applied Mathematics},
      volume = {6},
      number = {2},
      pages = {28-33},
      doi = {10.11648/j.ajam.20180602.11},
      url = {https://doi.org/10.11648/j.ajam.20180602.11},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajam.20180602.11},
      abstract = {An adjusted trinomial model for pricing both European and American arithmetic average-based Asian options is proposed. The Kamrad and Ritchken trinomial tree governs the underlying asset evolution. The algorithm selects a subset of the true averages realized at each node to serve as the representative averages. The option prices are then computed via backward induction and interpolation. The results show that the trinomial method produces more accurate prices especially in the case of European style Asian options.},
     year = {2018}
    }
    

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    AU  - Dennis Odhiambo Ogot
    AU  - Phillip Ngare
    AU  - Joseph Mung’atu
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    AB  - An adjusted trinomial model for pricing both European and American arithmetic average-based Asian options is proposed. The Kamrad and Ritchken trinomial tree governs the underlying asset evolution. The algorithm selects a subset of the true averages realized at each node to serve as the representative averages. The option prices are then computed via backward induction and interpolation. The results show that the trinomial method produces more accurate prices especially in the case of European style Asian options.
    VL  - 6
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