Approximating stochastic volatility by recombinant trees

Erd\.in\c{c} Aky{\i}ld{\i}r{\i}m, Yan Dolinsky and 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.

Date: 2012-05, Revised 2014-07
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Published in Annals of Applied Probability 2014, Vol. 24, No. 5, 2176-2205

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