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 suffer from exponential running time, inaccuracy, or other problems. Lyuu and Wu proved that the trinomial-tree option pricing algorithms of Ritchken and Trevor (1999) and Cakici and 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 and Wu (2003) still contains some problems. For example, the option prices suffer a trend to deviate from true values as n increases. This thesis proposes a new methodology to further improve the Lyuu-Wu algorithm by addressing this problem. We will confirm our algorithm’s efficiency and accuracy with numerical experiments.