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 , an LRB has the law of a Lévy bridge. We consider an asset that generates a cash-flow at . The information about is modelled by an LRB with terminal value . The price process of the asset is worked out, along with the prices of options.