Stochastic dividend yields and derivatives pricing in complete markets

Abstract

When an underlying yields a stochastic dividend yield, derivatives with linear payoff at their maturities that are written on this underlying have the following properties: (i) they have a unique price only if markets are complete; (ii) the dynamic strategies that replicate these contingent claims contain hedging components against the state variables in the economy; (iii) the prices of these derivatives will depend upon the dynamics of the market prices of risk even when markets are complete. Within an affine framework, we explicitly price forward and futures contracts with stochastic dividends. We also show that the quantitative impact of assuming that dividends are deterministic when they are actually stochastic is significant.