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Approximating stochastic volatility by recombinant trees

Author(s): Akyildirim, E; Dolinsky, Y; Soner, H Mete

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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.
Publication Date: 1-Jan-2014
Citation: Akyildirim, E, Dolinsky, Y, Soner, HM. (2014). Approximating stochastic volatility by recombinant trees. Annals of Applied Probability, 24 (5), 2176 - 2205. doi:10.1214/13-AAP977
DOI: doi:10.1214/13-AAP977
ISSN: 1050-5164
Pages: 2176 - 2205
Type of Material: Journal Article
Journal/Proceeding Title: Annals of Applied Probability
Version: Author's manuscript

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