GARCH-二元跳躍選擇權的樹狀評價法
A Tree-Based Algorithm for Option Pricing under GARCH-Binary Jump Processes
Date Issued
2006
Date
2006
Author(s)
Chen, Shin-Chiang
DOI
en-US
Abstract
This thesis proposes the first tree-based algorithm in the literature for the pricing of options under the GARCH-jump model. Following Duan, Ritchken, and Sun (2005), we propose a new model, the GARCH-binary jump option pricing model, with modifications on their jump distribution. In this new model, besides conditional heteroskedasticity, there are also binary jumps in the pricing kernel and correlated binary jumps in asset returns and volatilities. The high complexity and intractability in constructing a tree-based algorithm for GARCH-lognormal jump processes motivate the simple binary jump distribution assumption. When jumps are suppressed, our model nests Duan’s (1995) NGARCH option pricing model, where conditional returns are posited to be normal. When the GARCH effect is suppressed, the diffusion limit of our model converges to the binary jump-diffusion models of Amin (1993) and Trippi, Brill, and Harriff (1992). Following the binary jump-diffusion tree of Amin (1993), we superimpose binary jumps on a GARCH option pricing tree. Our choice of the tree is the mean-tracking (MT) tree proposed by Lyuu and Wu (2005). Both European and American options can then be priced by our algorithm. We give sufficient conditions for our algorithm to avoid the short-maturity problem inherit in the original GARCH option pricing tree of Ritchken and Trevor (1999) and Cakici and Topyan (2000). Furthermore, the tree size growth is guaranteed to be quadratic if the number of partitions of one day, n, does not exceed a threshold predetermined by the model parameters. This surprising finding places the tree-based GARCH-jump option pricing algorithm in the same complexity class as binomial trees under the Black-Scholes model. The level of efficiency makes the proposed model and algorithm practical. Furthermore, our algorithm can be naturally amended to alternative GARCH specifications. Extensive numerical evaluation is conducted to confirm the analytical results and the numerical accuracy of our algorithm. Numerical comparisons are also conducted between the GARCH-binary and lognormal jump models. Several implications are drawn from these results.
Subjects
樹狀演算法
選擇權評價
變異數異質性
二元跳躍
GARCH-Jump Process
Tree-Based Algorithm
Binary Jump
Type
thesis
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