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Approximating stochastic volatility by recombinant trees

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

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    File URL: http://arxiv.org/pdf/1205.3555
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    Paper provided by arXiv.org in its series Papers with number 1205.3555.

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    Date of creation: May 2012
    Date of revision: Jul 2014
    Publication status: Published in Annals of Applied Probability 2014, Vol. 24, No. 5, 2176-2205
    Handle: RePEc:arx:papers:1205.3555
    Contact details of provider: Web page: http://arxiv.org/

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