Joint risk liquidity/price analysis via Ito line integrals: a simulation study
by
Manuel L. Esquível
Dept. Mathematics FCT/UNL, Quinta da Torre, 2829-516 Caparica, Portugal.

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.

NB:to be presented at the Special Session on "Statistical and Stochastic Methods for Financial Mathematics"

Date received: January 31, 2008