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Title: Information-based models for finance and insurance
Author: Hoyle, Anthony Edward Vickerstaff
ISNI:       0000 0004 2693 8670
Awarding Body: Imperial College London
Current Institution: Imperial College London
Date of Award: 2010
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In financial markets, the information that traders have about an asset is reflected in its price. The arrival of new information then leads to price changes. The ‘information-based framework’ of Brody, Hughston and Macrina (BHM) isolates the emergence of information, and examines its role as a driver of price dynamics. This approach has led to the development of new models that capture a broad range of price behaviour. This thesis extends the work of BHM by introducing a wider class of processes for the generation of the market filtration. In the BHM framework, each asset is associated with a collection of random cash flows. The asset price is the sum of the discounted expectations of the cash flows. Expectations are taken with respect (i) an appropriate measure, and (ii) the filtration generated by a set of so-called information processes that carry noisy or imperfect market information about the cash flows. To model the flow of information, we introduce a class of processes termed Levy random bridges (LRBs), generalising the Brownian and gamma information processes of BHM. Conditioned on its terminal value, an LRB is identical in law to a Levy bridge. We consider in detail the case where the asset generates a single cash flow XT at a fixed date T. The flow of information about XT is modelled by an LRB with random terminal value XT. An explicit expression for the price process is found by working out the discounted conditional expectation of XT with respect to the natural filtration of the LRB. New models are constructed using information processes related to the Poisson process, the Cauchy process, the stable-1/2 subordinator, the variance-gamma process, and the normal inverse-Gaussian process. These are applied to the valuation of credit-risky bonds, vanilla and exotic options, and non-life insurance liabilities.
Supervisor: Hughston, Lane Sponsor: EPSRC ; European Science Foundation, Advanced Mathematical Methods in Finance programme (AMaMeF)
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral