This dissertation includes three topics. We first introduce the statistical properties of option pricing and literature related to the following topics. The first topic focuses on GARCH processes with Lévy innovation and their empirical analysis on TAIEX index options. Comparing to other popular option pricing models, the results show that the GARCH-Lévy processes fit well in-sample data. However, according to out-of- sample performances from three loss functions, there is no best model across all moneynesses. Although the VG option pricing model performs well at the money, the NGARCH option pricing model for in-the-money or out-of-the-money contracts is better than others.
The second topic studies two baskets options under a multivariate normal inverse Gaussian model. The value of a geometric basket option can be expressed as an analytic-form formula and then its hedge ratios can be obtained from the partial derivatives of its pricing formula. Similarly, the value of an arithmetic basket option can be expressed as an analytic-form formula and then its hedge ratios can be obtained from the partial derivatives of its pricing formula. These options can be further applied to price related products, for example, multifund unit-linked insurance contracts. The numerical result supports the internal consistency of our closed-form analytical expressions for two basket options on two assets.
The third topic studies the valuation of catastrophe insurance products. We survey the data about catastrophe events. Catastrophe occurrences can be forecasted, yet appear to have some rules, for example, the energy released by an earthquake can delay the next occurrence. Moreover, the 2-7 year cycle or pattern referred to as ENSO is a frequent natural reminder about the complex influences of the global ocean, atmosphere, and continental heat budget cycling and seasonality. The regime-switching compound Poisson process can be adopted to describe the jump-diffusion process under different states and thus be incorporated into the catastrophe loss or claim dynamics under different natural environments. Most catastrophe insurance contracts have provisions on some triggers to make loss claims or debt-forgiveness. Thus, we derive the pricing formulas of trigger options and then pricing catastrophe insurance products using an option-based method. The empirical evidences show that the regime-switching Poisson process in the RJSD model fits better than the pure Poisson process in a jump diffusion model in describing the arrival rates of great natural disasters over 1950-2006. We can further extend it to enough states to fit CAT arrival better, and then price other catastrophe insurance products more exactly.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-1028108-160333 |
| Date | 28 October 2008 |
| Creators | Wu, Yang-che |
| Contributors | Yu-Chuan Huang, So-De Shyu, Szu-Lang Liao |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | Cholon |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-1028108-160333 |
| Rights | unrestricted, Copyright information available at source archive |
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