A Pricing Formula for Delayed Claims: Appreciating the Past to Value the Future
21 Pages Posted: 19 May 2015 Last revised: 14 Jan 2019
Date Written: January 10, 2019
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 current market values of the past and the future, 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
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