Option Valuation with Normal Mixture GARCH Models
The class of mixture GARCH models introduced by Haas, Mittnik and Paollela (2004) and Alexander and Lazar (2006) provides a better alternative for fitting financial data than various other GARCH models driven by the normal or skewed t-distribution. In this paper we propose different option pricing methodologies when the underlying stock dynamic is modeled by an asymmetric normal mixture GARCH model with K volatility components. Since under GARCH models the market is incomplete there are an infinite number of martingale measures one can use for pricing. For our mixture setting we analyze the impact of three risk-neutral candidates: a generalized local risk neutral valuation relationship, an Esscher transform and an extended Girsanov principle. We investigate the out-of-sample performance of an asymmetric GARCH model with a mixture density of two normals for Call options written on the S&P 500 Index. The performance under all three transformations is quite impressive when compared to the benchmark GARCH model with normal driving noise. The overall improvement is explained not only by the skewness and leptokurtosis exhibited by the innovation mixture distribution, but also by the richer parametrization used in modeling the dynamics of the multi-component conditional volatility.
If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Volume (Year): 12 (2008)
Issue (Month): 2 (May)
|Contact details of provider:|| Web page: http://www.degruyter.com|
|Order Information:||Web: http://www.degruyter.com/view/j/snde|
When requesting a correction, please mention this item's handle: RePEc:bpj:sndecm:v:12:y:2008:i:2:n:5. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Peter Golla)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.