A Pricing Formula for Delayed Claims

Enrico Biffis, Beniamin Goldys, Cecilia Prosdocimi and Margherita Zanella

Abstract

We consider the valuation of contingent claims with delayed dynamics in a Black and Scholes complete market model. We find a pricing formula that can be decomposed into terms reflecting the market values of the past and the present, showing how the valuation of future cashflows cannot abstract away from the contribution of the past. As a practical application, we provide an explicit expression for the market value of human capital in a setting with wage rigidity.

Keywords: Stochastic functional differential equations, delay equations, no-arbitrage pricing, human capital, sticky wages.

AMS Subject Classification: Primary 34K50; secondary 91B25, 91G80.