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Pricing and hedging GDP-linked bonds in incomplete markets

Author

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  • Andrea Consiglio

    (University of Palermo)

  • Stavros A Zenios

    (University of Cyprus and Wharton Financial Institutions Center)

Abstract

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 by-product of the model we obtain a hedging portfolio. Using linear programming duality we compute also 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 sensitivity analysis of prices and risk premia to the risk factors and bond design parameters. We also compare coupon-indexed and principal-indexed bonds. Further results with calibrated instruments for Germany, Italy and South Africa shed light on a policy question, whether the risk premia of these bonds make them beneficial for sovereigns. Our findings affirm that designs are possible for both coupon-indexed and principal-indexed bonds that 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.

Suggested Citation

  • Andrea Consiglio & Stavros A Zenios, 2018. "Pricing and hedging GDP-linked bonds in incomplete markets," Working Papers 29, European Stability Mechanism.
  • Handle: RePEc:stm:wpaper:29
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    References listed on IDEAS

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    Cited by:

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    2. Andrea Consiglio & Michele Tumminello & Stavros A. Zenios, 2018. "Pricing Sovereign Contingent Convertible Debt," Journal of Enterprising Culture (JEC), World Scientific Publishing Co. Pte. Ltd., vol. 21(08), pages 1-36, December.
    3. Jean-Marc Fournier & Jakob Lehr, 2018. "Issuing GDP-linked bonds: Supply and demand can match," OECD Economics Department Working Papers 1500, OECD Publishing.
    4. Nicolas Carnot & Stéphanie Pamies Sumner, 2017. "GDP-linked Bonds: Some Simulations on EU Countries," European Economy - Discussion Papers 2015 - 073, Directorate General Economic and Financial Affairs (DG ECFIN), European Commission.
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    More about this item

    Keywords

    contingent bonds; debt restructuring; asset pricing; incomplete markets; risk premia; stochastic programming; super-replication;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • D61 - Microeconomics - - Welfare Economics - - - Allocative Efficiency; Cost-Benefit Analysis
    • E3 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles
    • E47 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Forecasting and Simulation: Models and Applications
    • E62 - Macroeconomics and Monetary Economics - - Macroeconomic Policy, Macroeconomic Aspects of Public Finance, and General Outlook - - - Fiscal Policy
    • F34 - International Economics - - International Finance - - - International Lending and Debt Problems
    • G21 - Financial Economics - - Financial Institutions and Services - - - Banks; Other Depository Institutions; Micro Finance Institutions; Mortgages
    • G38 - Financial Economics - - Corporate Finance and Governance - - - Government Policy and Regulation
    • H63 - Public Economics - - National Budget, Deficit, and Debt - - - Debt; Debt Management; Sovereign Debt

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