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Barrier Option Pricing Using Adjusted Transition Probabilities

Author

Listed:
  • Giovanni Barone-Adesi

    (University of Lugano and Swiss Finance Institute)

  • Nicola Fusari

    (University of Lugano and Swiss Finance Institute)

  • John Theal

    (University of Lugano and Swiss Finance Institute)

Abstract

In the existing literature on barrier options, much effort has been exerted to ensure convergence through placing the barrier in close proximity to, or directly onto, the nodes of the tree lattice. In this paper we show that this may not be necessary to achieve accurate option price approximations. Using the Cox/Ross/Rubinstein binomial tree model and a suitable transition probability adjustment we demonstrate that our “probability-adjusted” model exhibits increased convergence to the analytical option price. We study the convergence properties of various types of options including (but not limited to) double knock-out, exponential barrier, double (constant) linear barriers and linear time-varying barriers. For options whose strike price is close to the barrier we are able to obtain numerical results where other models fail and, although convergence tends to be slow, we are able to calculate reasonable approximations to the analytical option price without having to reposition the lattice nodes.

Suggested Citation

  • Giovanni Barone-Adesi & Nicola Fusari & John Theal, "undated". "Barrier Option Pricing Using Adjusted Transition Probabilities," Swiss Finance Institute Research Paper Series 07-02, Swiss Finance Institute.
  • Handle: RePEc:chf:rpseri:rp0702
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    File URL: http://papers.ssrn.com/sol3/papers.cfm?abstract_id=964623
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    More about this item

    Keywords

    barrier option; binomial tree; convergence rate; transition probability;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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