Y.-D. Lyuu and C.-N. Wu (Taiwan)
: GARCH, trinomial tree, path depen dency, option
The trinomial-tree GARCH option pricing algorithm of Ritchken and Trevor (1999) is claimed to be effi cient. That algorithm is subsequently modified by Ca kici and Topyan (2000). This paper proves that both algorithms explode exponentially when the number of partitions per day, n, exceeds a typically small num ber determined by the GARCH parameters. Worse, when explosion happens, the tree cannot grow beyond a certain maturity date, making it unable to price derivatives with a longer maturity. The cut-off ma turity shortens very fast with increasing n. Hence the algorithms must be limited to using small n's, which unfortunately has accuracy problems. These findings throw into question some of the calculated prices in the literature. Numerical data confirm the theoretical results. The problem of provably efficient tree-based GARCH option pricing algorithms remains open.
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