In the first essay (Chapter 2), we develop an efficient payoff function approximation approach to estimating lower and upper bounds for pricing American arithmetic average options with a large number of underlying assets. This method is particularly efficient for asset prices modeled by jump-diffusion processes with deterministic volatilities because the geometric mean is always a one-dimensional Markov process regardless of the number of underlying assets and thus is free from the curse of dimensionality. Another appealing feature of our method is that it provides an extremely efficient way to obtain tight upper bounds with no nested simulation involved as opposed to some existing duality approaches. Various numerical examples with up to 50 underlying stocks suggest that our algorithm is able to produce computationally efficient results. Chapter 3 solves portfolio choice problem in multi-dimensional jump-diffusion models designed to capture empirical features of stock prices and financial contagion effect. To obtain closed-form solution, we develop a novel general decomposition technique with which we reduce the problem into two relative simple ones: Portfolio choice in a pure-diffusion market and in a jump-diffusion market with less dimension. The latter can be reduced further to be a bunch of portfolio choice problems in one-dimensional jump-diffusion markets. By virtue of the decomposition, we obtain a semi-closed form solution for the primary optimal portfolio choice problem. Our solution provides new insights into the structure of an optimal portfolio when jumps are present in asset prices and/or their variance-covariance. In Chapter 4, we develop a estimation procedure based on Markov Chain Monte Carlo methods and aim to provide systematic ways to estimating general multivariate stochastic volatility models. In particular, this estimation technique is proved to be efficient for multivariate jump-diffusion process such as the model developed in Chapter 3 with various simulation studies. As a result, it contributes to the asset pricing literature by providing an efficient estimation technique for asset pricing models.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:731305 |
| Date | January 2016 |
| Creators | Yang, Cheng-Yu |
| Publisher | University of Warwick |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://wrap.warwick.ac.uk/93986/ |
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