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Simulating the impact of state-contingent debt instruments on sovereign finances: An Excel toolkit

State-contingent debt instruments could provide sovereigns with additional policy space in bad states of the world. This column presents an Excel-based tool that allows debt managers and investors to explore the impact of different designs of such instruments on public debt and gross financing needs under user-specified macroeconomic scenarios (both baseline and shocks). Illustrative results show the potential benefits of different bond designs on both debt and gross financing needs.

Sovereign state-contingent debt instruments (SCDIs) are instruments that link the issuer’s contractual debt service obligations to a pre-defined state variable, and are designed to alleviate pressure on sovereign finances in bad states of the world. While several previous studies (e.g. Barr et al. 2014, Blanchard et al. 2016, Sandleris et al. 2008) have conducted simulations of the potential impact of SCDIs on public debt, these papers have generally focused on individual designs of SCDIs, have only included one-period debt, abstracted from gross financing needs, or have made restrictive assumptions about the behaviour of interest rates and/or expectations for the state variable.

As a complement to those approaches, this column presents a simple Excel-based tool, which can be used to examine the implications of three benchmark designs of multi-period state-contingent debt.  The tool takes a user-specified macro-framework and produces simulations of the path of both public debt and gross financing needs (GFNs) under each of the three SCDI designs, and for different shares of state-contingent and conventional debt. The tool can be found here.

Sovereign financing with three benchmark SCDIs

As discussed in a companion VoxEU column (Ali Abbas et al. 2017), IMF (2017) proposes three benchmark designs that could balance the needs of specific issuers and investors. While there are various possibilities for the state variable in each design, for comparability we focus on the three variants in which returns are tied to nominal GDP.

The ‘linker’ design is such that both the principal and coupon on this bond are linked to an index ratio, determined by the cumulative growth of GDP since the bond’s issue.  This structure is akin to a standard inflation-linked bond, but with the GDP level, rather than a consumer price index, as the state variable.

The second design is the ‘floater’. This bond has a fixed principal, but the coupon in each year is tied to the GDP growth rate.  On technical grounds, a coupon floor of zero would likely be needed, but the issuer could also set a coupon floor above zero, and/or apply a coupon cap to limit upside payments.

Finally, in the ‘extendible’ design, the coupon and principal are fixed, but the bond’s maturity is extended by a few years if GDP falls by more than a specified percentage.1

To model sovereign financing in each case, the tool specifies that both the initial debt stock and the flow of financing in each subsequent period are composed of a (customisable) mix of conventional bonds and SCDIs. It also specifies that both conventional bonds and SCDIs are issued at a single maturity, which can be modified, and calibrated to match the average maturity of an issuer’s existing debt. Also, coupons on each SCDI are determined using a discounted cash flow framework to calculate the present value of each SCDI at issuance.2

Expected principal and interest payments are calculated based on assumptions about the investor’s central expectations for nominal GDP growth, which are then discounted using the interest rate on conventional bonds, plus a (customizable) yield premium. The determination of these yield premiums, interest rates, and investor expectations is discussed in more detail below.

Specifying a macroeconomic scenario

To simulate the path of debt and financing needs under different sovereign financing assumptions, a macro-economic scenario is needed.3

The SCDI tool allows users to input initial conditions for several key macroeconomic variables, which can be calibrated to the country under consideration. These include the initial levels of debt, primary expenditures, revenues and nominal GDP.4

A baseline path for nominal GDP and interest rates is then generated, under the assumption that both nominal GDP growth and interest rates are constant at user-specified rates.

To complete the macroeconomic framework, the tool also introduces a link between government deficits and GDP. Specifically, it is assumed that government revenue growth moves one-for-one with GDP growth, while government expenditure is set to bring the primary balance towards a “debt-stabilising” level in the medium term.5

The user can then choose to apply a macroeconomic shock to this baseline.  The template allows users to implement two types of shock to nominal GDP. A level shock affects the growth rate of GDP for a single period, but has no impact on GDP growth in future periods. A growth shock affects the GDP growth rate for a user-specified number of years following the ‘level’ shock.

These two shocks can be combined flexibly to generate alternative scenarios.  For example, a purely ‘cyclical’ shock, where the level of GDP returns to its pre-shock trend, can be modelled by applying a negative level shock, followed by a positive growth shock in the recovery period.  Conversely, a recession followed by slower growth, as experienced by many countries following the Global Crisis, would correspond to a negative level shock combined with a negative growth shock.

Although the tool does not model a direct response of interest rates to GDP shocks – which is likely to be highly variable across countries, and dependent on a country’s monetary policy framework – there is an (optional) interaction between the interest rates on conventional bonds and the rate of debt accumulation.6 When activated, this provides a further channel through which SCDIs can reduce indebtedness – either via a slower pace of debt accumulation, and hence a smaller rise in interest rates (under the Linker and Floater), or by delaying re-financing until interest rates have fallen back (the Extendible).

Investor expectations and yield premiums

The behaviour of both investor expectations for the state variable, and the yield premiums investors demand to hold SCDIs, are of vital importance in the analysis of state contingent instruments. Ultimately, the return on a given SCDI is determined not just by nominal GDP outturns, but by whether these outturns are higher or lower than expected by the investor at the time of issuance, and the size of any (ex-ante) yield premium. As such, the average level of the yield premium, and the behaviour of both investor expectations and premiums in the face of macroeconomic shocks, will determine the degree of relief the instruments provide.

The likely yield premiums on SCDIs are highly uncertain, and are likely to vary for different instrument designs and by country. For example, Table 1 summarises a range of CAPM-based estimates of the premium investors might demand for GDP-volatility (IMF 2017). On top of a GDP-volatility premium, investors might demand additional premiums to compensate for the novelty and lower liquidity of SCDIs, at least initially. Similarly, the option premium for extendible debt is likely to vary by country and over time, reflecting, among other factors, the choice of trigger, the joint distribution of interest rates and the trigger variable, and the size of any step-up coupon.

Table 1 Estimates of the volatility risk premium on GDP-linked bonds (CAPM)

To help users assess these issues, the tool several features. An expectations parameter, λ, governs the degree to which investors anticipate the growth shocks following the initial shock period.  If λ=1, then following the level shock, the growth shocks in subsequent periods are fully anticipated by investors. Conversely, if λ=0 growth expectations are set adaptively, based on past growth rates.7 For intermediate values of λ, expectations are a weighted average of the ‘full anticipation’ and ‘adaptive’ cases. Secondly, there is a customisable average yield premium on each SCDI, and sensitivity analysis to demonstrate the impact of variations in these premiums. Finally, the model includes the option to explore the implications of a user-specified time-varying path for risk premiums.8  However, by default, the tool generates simulations under the assumption of constant SCDI yield premiums.

Illustrative results

To demonstrate how the tool can be used, we present a set of results calibrated for an economy with an initial debt-to-GDP ratio of 100%. We then apply a 7% level shock, followed by a 1.5% growth shock.9

Figure 1 presents a panel of charts produced by the tool, comparing debt-to-GDP and GFN-GDP under each design, for a given yield premium and share of SCDIs in the portfolio. The results differ depending on the characteristics of each instrument.

Figure 1 Public debt and GFNs with three benchmark SCDIs

Linkers can substantially reduce the impact of the shock on the debt-to-GDP ratio, but have little immediate impact on gross financing needs.

Floaters also generate substantial solvency relief, although the total impact on debt is lower because the zero-coupon floor binds in the first shock year.  However, the floating coupon also mitigates the initial impact of the level shock on GFNs.

Extendibles generate only very modest solvency relief, but provide more substantial liquidity relief, reflected in a marked reduction in GFNs in the immediate aftermath of the ‘level’ shock.

To allow further scrutiny of these results, the tool also produces three tables showing how debt-to-GDP (for the Linker and Floater) and GFN-to-GDP (for the Extendible) vary in the share of each SCDI in sovereign financing, and in the yield premium (Figure 2).

 For both Linkers and Floaters, a larger share in sovereign financing would result in a substantially lower Debt-to-GDP ratio. However, a yield premium of around 1% would offset much of these gains, and a premium of 2% would leave debt substantially higher than in the case with only conventional debt.

For Extendibles, a larger share in financing could substantially increase the sovereign’s liquidity relief. Here, GFNs are less sensitive to the assumed premium, but there is a modest decline in the amount of relief as the premium increases.

 Figure 2 Sensitivity to yield premiums and the share of SCDIs in financing

Authors’ note: This column draws on the main findings of a recent IMF (2017) board paper on “State-contingent debt instruments for sovereigns”. The views expressed in this column are those of the authors and should not be attributed to the IMF, its Executive Board, or its management. Any errors and omissions are the sole responsibility of the authors.


Ali Abbas, S M, D Hardy, J Kim and A Pienkowski (2017), “State-contingent debt instruments for sovereigns: A balanced view”,, 6 June.

Aisen, A, and D Hauner (2008), “Budget Deficits and Interest Rates: A Fresh Perspective”, IMF Working Paper WP/08/42.

Barr, D, O Bush, and A Pienkowski (2014), “GDP-linked bonds and sovereign default”, Bank of England Working Paper, No. 484, January.

Blanchard, O, P Mauro and J Acalin (2016), “The case for growth indexed bonds in advanced economies”, Peterson Institute for International Economics, Policy Brief, No. 16-2, February.

Bowman, J, and P Naylor (2016), “GDP-Linked Bonds”, Reserve Bank of Australia Bulletin, September Quarter.

Campbell, J Y, and R Shiller (1988), “The Dividend-Price Ratio and Expectations of Future Dividends and Discount Factors”, Review of Financial Studies, 1, 195-227.

Kamstra, M, and R Shiller (2009), “The Case for Trills: Giving the People and their Pension Funds a Stake in the Wealth of the Nation”, Cowles Foundation Discussion Paper No. 1717.

IMF (2017), “State-Contingent Debt Instruments for Sovereigns”, IMF Policy Paper, 22 May, Washington.

Philippon, T (2009), “The Bond Market's q”, The Quarterly Journal of Economics, Oxford University Press, 124(3), 1011-1056.

Sandleris, G, H Sapriza and F Taddei (2008), “Indexed sovereign debt: an applied framework”, Collegio Carlo Alberto Working Paper No. 104.


[1] The tool also allows for a ‘step-up’ coupon on the extended bond.

[2] The tool contains a fuller explanation of these pricing assumptions, including the setting of other parameters, such as the ‘principal factor’ described in the “London Term Sheet”, which is relevant for the linker and floater designs.

[3] There may also be feedback between the macro-economic scenario and the form of financing.  For example, in countries with limited fiscal space, the presence of SCDIs in the portfolio might allow greater use of countercyclical fiscal policies to mitigate the fall in GDP. For comparability, we assume that fiscal policy is the same regardless of the mix of SCDI and conventional debt financing, but in practice countercyclical fiscal policy is a key channel through which SCDIs could deliver benefits.

[4] For simplicity, this framework abstracts from exchange rates and the presence of FX debt.  However, the Extendible bond might be particularly appropriate for countries with significant FX borrowing, and the tool can still give a sense of the marginal financing relief that could be obtained in the event of a maturity extension.

[5] That is, the level of the primary balance that would maintain debt/GDP at its level in the previous period, given expectations for future growth and interest rates. Specifically, we assume that the ‘gap’ between the actual primary balance and the ‘debt-stabilizing’ level follows an AR(1) process, with a coefficient of 0.7, implying that half of the gap will close within 2 years.

[6] Specifically, this calibration is based on Aisen and Hauner (2008), although we apply this coefficient to changes in the debt-to-GDP ratio rather than the primary deficit-to-GDP ratio.

[7] For growth expectations over a horizon M, the adaptive formulation assumes that expectations are equal to average growth over the last M periods, excluding the period of the level shock.

[8] Empirical studies suggest that risk premiums on equities (Campbell and Shiller 1988) and corporate bonds (Philippon 2008) move pro-cyclically, which might suggest that similar movements would apply to SCDIs.

[9] For completeness, we describe here the full parametrization underlying these simulations. ‘Trend’ nominal GDP growth is set at 4%, while nominal interest rates are set at 4.5% in the baseline. Initial government revenue-to-GDP is 40%, and primary expenditure-to-GDP is also 40%. The first simulation year is 2017, and a -7% level shock is applied in 2020 (i.e. there is a 3% GDP contraction), followed by a -1.5% growth shock from 2021 onwards. The expectations parameter, λ, is set at 0.5. The maturity of all instruments modelled is 7 years, and the yield premium on the Linker and Floater is 0.25%. The yield premium on the Extendible is 0.5%, and the trigger is set at -1% growth, so that the maturity extensions are triggered in 2020, but there are no further extensions in subsequent years. The maturity extension length is 3 years, and there is no ‘step-up’ coupon.

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