Pricing and hedging GDP-linked bonds in incomplete markets
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Working Paper 29
This paper shows how to design, price, and hedge GDP-linked bonds and provides favourable evidence for their use, based on results for both advanced economies and emerging markets.
Authors: Andrea Consiglio (University of Palermo) and Stavros A. Zenios (University of Cyprus and Wharton Financial Institutions Center, University of Pennsylvania)
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.
Disclaimer: This Working Paper should not be reported as representing the views of the ESM. The views expressed in this Working Paper are those of the author(s) and do not necessarily represent those of the ESM or ESM policy. No responsibility or liability is accepted by the ESM in relation to the accuracy or completeness of the information, including any data sets, presented in this Working Paper.
Keywords: Contingent bonds, debt restructuring, asset pricing, incomplete markets, risk premia, stochastic programming, super-replication
JEL codes: C61, C63, D61,E3, E47, E62, F34, G21, G38, H63