Keynesian resurgence: financial stimulus and contingent claims modelling

Since the commencement of the Global Financial Crisis, a worldwide resurgence in applying Keynesian modelling has occurred, and has been cited as a major factor in averting a worldwide economic depression. A key aspect of Keynesian modelling is that governments gain contingent claims on firms in exchange for financial stimulus. However, there exist few mathematical finance models examining Keynesian modelling, stimulus modelling and the valuation of such government contingent claims. In this paper we provide a new mathematical finance framework for modelling firms and financial stimulus under a Keynesian framework; we apply a stochastic differential equation model, rather than the standard time series models. Our model incorporates fundamental concepts of Keynesian modelling and Keynesian stimulus, which is a new characteristic to current financial models. We model the government's contingent claim on the firm as a real call option, and derive a closed form solution for the value of this option which takes into account firm stimulus. We also derive a solution for the minimum firm value required to exercise the option. We conduct numerical experiments for different firm equilibrium values, firm values, economic cycles and analyse the impact on option and stimulus values.