Forward Backward Stochastic Model of Financial Asset Pricing with Idiosyncratic Noise

Abstract

A new acceptable price approach to stochastic endpoint determination at given horizon accounting for the marginal investor beliefs and behaviour was proposed. Two-sided filtration with FBSDE defined stochastic dynamics was formulated for acceptable asset price under the risk-neutral probability measure, at that the target price distribution is characterized by the averaged over active market agent subset parameters. For the current price at market equilibrium, the acceptable price of risk distribution was found. The implied volatility dependencies for the equilibrium conditions and with predicted utility and liquidity premiums were determined. A generalized solution for the forward-backward stochastic problem and a partial solution for the formulated for options stochastic terminal conditions were found. The deep learning algorithm with simulated idiosyncratic noise was tested.

Keywords: Marginal investor behavior, Forward-backward stochastic differential equation, Market equilibrium, Bond pricing, Derivative pricing, Neural network with idiosyncratic noise.

JEL Classification: C53, C62, D53, G12, G13, G40.