On Accurate Trinomial GARCH Option Pricing Algorithms

The GARCH model has been successful in describing the volatility dynamics of asset return series. However, tree-based GARCH option pricing algorithms su®er from exponential running time, inaccuracy, or other problems. Lyuu & Wu proved that the trinomial-tree option pricing algorithms of Ritchken & Trevor (1999) & Cakici & Topyan (2000) explode exponentially when
the number of partitions per day, n, exceeds a threshold determined by the GARCH parameters. The improved algorithm of Lyuu & Wu (2003) still
contains some problems. For example, the option prices su®er a trend to deviate from true values as n increases. This thesis proposes a new method-
ology to further improve the Lyuu-Wu algorithm by addressing this problem. We will confirm our algorithm's e±ciency & accuracy with numerical experiments.