A Pricing Formula for Delayed Claims: Appreciating the Past to Value the Future

26 Pages Posted: 19 May 2015 Last revised: 29 Dec 2022

See all articles by Enrico Biffis

Enrico Biffis

Imperial College Business School

Ben Goldys

The University of Sydney

Cecilia Prosdocimi

Luiss Guido Carli University

Margherita Zanella

Luiss Guido Carli University

Date Written: December 26, 2022

Abstract

We consider the valuation of contingent claims with delayed dynamics in a Samuelson 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 prospective
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. The formula we derive has successfully been used to explicitly solve the infinite
dimensional stochastic control problems addressed in [7], [6] and [16].

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

Suggested Citation

Biffis, Enrico and Goldys, Ben and Prosdocimi, Cecilia and Zanella, Margherita, A Pricing Formula for Delayed Claims: Appreciating the Past to Value the Future (December 26, 2022). Available at SSRN: https://ssrn.com/abstract=2607892 or http://dx.doi.org/10.2139/ssrn.2607892

Enrico Biffis

Imperial College Business School ( email )

Imperial College London
South Kensington campus
London, SW7 2AZ
United Kingdom

Ben Goldys (Contact Author)

The University of Sydney ( email )

University of Sydney
Sydney, NSW 2006
Australia

Cecilia Prosdocimi

Luiss Guido Carli University ( email )

Via O. Tommasini 1
Rome, Roma 00100
Italy

Margherita Zanella

Luiss Guido Carli University ( email )

Via O. Tommasini 1
Rome, Roma 00100
Italy

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