Endogenous emergence of coincidence points of market participants' expectations in stochastic models: from implicit equation to computational method
Abstract:
The paper proposes a model for the dynamics of two price levels of \\ expectations of large financial market participants. The moments when these levels coincide (bifurcation) arise endogenously as a consequence of an implicit stochastic equation driven by a Wiener process. The main result is a computational method that allows finding all possible expectation levels without analytically solving the original equation. The original problem is reduced to a deterministic ordinary differential equation, for which a combination of shooting and Newton methods is proposed. This approach works efficiently at bifurcation points and allows tracing the non-uniqueness of solutions. The application of the model to risk assessment of derivative financial instruments is discussed, where knowledge of all expectation levels makes it possible to construct distributions of future prices.
