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Approximating stochastic volatility by recombinant trees

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  • Erd.inc{c} Aky{i}ld{i}r{i}m
  • Yan Dolinsky
  • H. Mete Soner

Abstract

A general method to construct recombinant tree approximations for stochastic volatility models is developed and applied to the Heston model for stock price dynamics. In this application, the resulting approximation is a four tuple Markov process. The first two components are related to the stock and volatility processes and take values in a two-dimensional binomial tree. The other two components of the Markov process are the increments of random walks with simple values in $\{-1,+1\}$. The resulting efficient option pricing equations are numerically implemented for general American and European options including the standard put and calls, barrier, lookback and Asian-type pay-offs. The weak and extended weak convergences are also proved.

Suggested Citation

  • Erd.inc{c} Aky{i}ld{i}r{i}m & Yan Dolinsky & H. Mete Soner, 2012. "Approximating stochastic volatility by recombinant trees," Papers 1205.3555, arXiv.org, revised Jul 2014.
  • Handle: RePEc:arx:papers:1205.3555
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    Cited by:

    1. Leippold, Markus & Schärer, Steven, 2017. "Discrete-time option pricing with stochastic liquidity," Journal of Banking & Finance, Elsevier, vol. 75(C), pages 1-16.
    2. Nikolai Dokuchaev, 2015. "On statistical indistinguishability of complete and incomplete discrete time market models," Papers 1505.00638, arXiv.org.

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