An Intrinsic Value Approach to Valuation with Forward–Backward Loops in Dividend Paying Stocks

We formulate a claim valuation problem where the dynamics of the underlying asset process contain the claim value itself. The problem is motivated here by an equity valuation of a firm, with intermediary dividend payments that depend on both the underlying, that is, the assets of the company, and the equity value itself. Since the assets are reduced by the dividend payments, the entanglement of claim, claim value, and underlying is complete and numerically challenging because it forms a forward–backward stochastic system. We propose a numerical approach based on disentanglement of the forward–backward deterministic system for the intrinsic values, a parametric assumption of the claim value in its intrinsic value, and a simulation of the stochastic elements. We illustrate the method in a numerical example where the equity value is approximated efficiently, at least for the relevant ranges of the asset value.