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arXiv · 1205.3555

Approximating stochastic volatility by recombinant trees

Erdinç Akyıldırım·Yan Dolinsky·H. Mete Soner
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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.

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Erdinç Akyıldırım, Yan Dolinsky, H. Mete Soner. 2012-05-16. Approximating stochastic volatility by recombinant trees. https://doi.org/10.1214/13-aap977

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