Securitization and equilibrium pricing under relative performance concerns

We investigate the effects of a finite set of agents interacting socially in an equilibrium pricing mechanism. A derivative written on non-tradable underlyings is introduced to the market and priced in an equilibrium framework by agents who assess risk using convex dynamic risk measures expressed by Backward Stochastic Differential Equations (BSDE). An agent is not only exposed to financial and non-financial risk factors, but he also faces performance concerns with respect to the other agents. The equilibrium analysis leads to systems of fully coupled multi-dimensional quadratic BSDEs.

Within our proposed models we prove the existence and uniqueness of an equilibrium. We show that aggregation of risk measures is possible and that a representative agent exists. We analyze the impact of the problem's parameters in the pricing mechanism, in particular how the agent's concern rates affect prices and risk perception.