On Accurate and Provably Efficient GARCH Option Pricing Algorithms
Date Issued
2005
Date
2005
Author(s)
Wu, Chi-Ning
DOI
20060927122855648546
Abstract
The GARCH model has been very successful in capturing the serial correlation of asset return volatilities. As a result, applying the model to options pricing attracts a lot of attention. However, previous tree-based GARCH option pricing algorithms suffer from exponential running time, a cut-off maturity, inaccuracy, or some ombination thereof. Specifically, this paper proves that the popular 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. Furthermore, when explosion happens, the tree cannot grow beyond a certain maturity date, making it unable to price derivatives with a longer maturity. As a result, the algorithms must be limited to using small n, which may have accuracy problems. The paper presents an alternative trinomialtree
GARCH option pricing algorithm.
Subjects
GARCH
trinomial tree
path dependency
option pricing
generating function
Publisher
臺北市:國立臺灣大學資訊工程學系
Type
report
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