This thesis studies the use of Lévy processes for option pricing and portfolio allocation problem. First, a new Geometric Lévy model is proposed to capture the volatility smirk exhibited by index options. To solve the new model, an efficient numerical algorithm is adopted, which can be applied to any time-changed Lévy model. It is the first attempt to model multi-scale volatility along with the leverage effect, based on pure jump processes. Calibration results show that the proposed model exhibits excellent performance. Second, the dynamic portfolio choice problem in a jump-diffusion model is considered, where an investor may face constraints on her portfolio weights. With several examples, the impact of no-short-selling and/or no-borrowing constraints on the performance of optimal portfolio strategies is examined. Last, the portfolio allocation problem is reconsidered with a new multi-variate jump-diffusion model, while the effect of asymmetric correlation is taken into account Empirical results show that the new model fits asymmetric correlations well. By allowing investment constraints, the economic loss of ignoring asymmetric dependence is evaluated. An explanation for the under-diversification problem is provided, concerning the risk caused by asymmetric correlations.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:632876 |
| Date | January 2014 |
| Creators | Zhang, Kun |
| Publisher | University of Warwick |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://wrap.warwick.ac.uk/63937/ |
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