Pricing and Hedging GDP-Linked Bonds in Incomplete Markets

22 Pages Posted: 11 May 2017 Last revised: 11 Oct 2021

See all articles by Andrea Consiglio

Andrea Consiglio

University of Palermo - d/SEAS

Stavros A. Zenios

Durham University Business School; University of Cyprus; Cyprus Academy of Sciences, Letters, and Arts; Bruegel

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Date Written: September 1, 2017


We model the super-replication of payoffs linked to a country's GDP as a stochastic linear program on a discrete time and state-space scenario tree to price GDP-linked bonds. As a byproduct of the model, we obtain a hedging portfolio. Using linear programming duality we also compute the risk premium. The model applies to coupon-indexed and principal-indexed bonds, and allows the analysis of bonds with different design parameters (coupon, target GDP growth rate, and maturity). We calibrate for UK and US instruments and carry out a sensitivity analysis of prices and risk premia to the risk factors and bond design parameters. We also compare coupon-indexed and principal-indexed bonds.

Results shed light on the policy question whether the risk premia of these bonds make them beneficial for sovereigns. The findings from UK and US data affirm that both coupon-indexed and principal-indexed bonds can benefit a sovereign, with an advantage for coupon-indexed bonds. This finding is robust, but a nuanced reading is needed due to the many inter-related risk factors and design parameters that affect prices and premia.

Keywords: contingent bonds, debt restructuring, asset pricing, incomplete markets, risk premium, stochastic programming, super-replication

JEL Classification: C61, C63, D61,E3, E47, E62, F34, G21, G38, H63

Suggested Citation

Consiglio, Andrea and Zenios, Stavros A., Pricing and Hedging GDP-Linked Bonds in Incomplete Markets (September 1, 2017). Journal of Economic Dynamics and Control, Available online Jan. 5, 2018. DOI:10.1016/j.jedc.2018.01.001, Available at SSRN: or

Andrea Consiglio

University of Palermo - d/SEAS ( email )

Viale delle Scienze, edificio 13
Palermo, 90124


Stavros A. Zenios (Contact Author)

Durham University Business School ( email )

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University of Cyprus ( email )

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Cyprus Academy of Sciences, Letters, and Arts ( email )


Bruegel ( email )

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