Lévy random bridges and the modelling of financial information

The information-based asset-pricing framework of Brody-Hughston-Macrina (BHM) is extended to include a wider class of models for market information. To model the information flow, we introduce a class of processes called Lévy random bridges (LRBs), generalising the Brownian bridge and gamma bridge information processes of BHM. Given its terminal value at T, an LRB has the law of a Lévy bridge. We consider an asset that generates a cash-flow XT at T. The information about XT is modelled by an LRB with terminal value XT. The price process of the asset is worked out, along with the prices of options.Lévy processes Lévy bridges Information-based asset pricing Option pricing Non-linear filtering theory