Information-based models for finance and insurance
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 L\'evy 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 L\'evy bridge. We consider in detail the case where the asset generates a single cash flow $X_T$ at a fixed date $T$. The flow of information about $X_T$ is modelled by an LRB with random terminal value $X_T$. An explicit expression for the price process is found by working out the discounted conditional expectation of $X_T$ 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.
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