Joint risk liquidity/price analysis via Ito line integrals: a simulation study
by
Manuel L. Esquivel
Department of Mathematics, Faculty of Science and Technology, New University of Lisbon

In previous work we introduced a way of jointly studying the risk evolution of two random quantities, given by diffusion processes, by means of an Ito line integral over the random curve specified by the these processes.

An application of the formalism so introduced to real data of portuguese stocks allowed us to plainly differentiate the joint liquidity/price risk profile of three stocks in a more precise way than using solely liquidity or risk.

In this work, after reviewing the main properties of the model introduced, we present a result on the existence and unicity of solutions for stochastic differential equations using the Ito line calculus developed previously.

We present a simulation study which highlights the properties of differentiation of the risk profiles under the assumption of different models for the evolution of the liquidity, of the price and of the risk process.

Date received: July 31, 2006