Scenario-generation methods for an optimal public debt strategy

Bernaschi, Massimo; Briani, Maya; Papi, Marco; Vergni, Davide

doi:10.1080/14697680601038167

Cited by 15 publications

(14 citation statements)

References 18 publications

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“…Consequently, while Amadori's condition is verified, e.g., by the Bernaschi et al [9] model of correlated interest rate factors, it is not verified, e.g., by the Heston model (which, incidentally, does not satisfy the uniform Lipschitz assumption either). In addition, Amadori's condition rules out the possibility that the diffusion matrix a is identically zero in a direction orthogonal to the boundary, as is the case for Asian options.…”

Section: The Bates Model With Downward Jumps In the Volatilitymentioning

confidence: 94%

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Singular risk-neutral valuation equations

2011

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Many risk-neutral pricing problems proposed in the finance literature do not admit closed-form expressions and have to be dealt with by solving the corresponding partial integro-differential equation. Often, these PIDEs have singular diffusion matrices and coefficients that are not Lipschitz-continuous up to the boundary. In addition, in general, boundary conditions are not specified. In this paper, we prove existence and uniqueness of (continuous) viscosity solutions for linear PIDEs with all the above features, under a Lyapunov-type condition. Our results apply to European and Asian option pricing, in jump-diffusion stochastic volatility and path-dependent volatility models. We verify our Lyapunov-type condition in several examples, including the arithmetic Asian option in the Heston model.

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Section: The Bates Model With Downward Jumps In the Volatilitymentioning

confidence: 94%

“…Correlated interest rate factors Recently Bernaschi et al [9] proposed an n-factor term structure model for valuing public debt securities where each factor follows a CIR-type model, but the driving Brownian motions are correlated. Then the n-dimensional factor process is not affine.…”

Section: The Bates Model With Downward Jumps In the Volatilitymentioning

confidence: 99%

Singular risk-neutral valuation equations

2011

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“…In Bernaschi et al (2007) is described a simulation model for the debt issuance, where the main economic risk factor is given by the interest rate. They adopt a mean reverting model for the term structure and link the fluctuations to a model for the official rate issued by the European Central Bank (ECB).…”

Section: Introductionmentioning

confidence: 99%

A stochastic programming model for the optimal issuance of government bonds

Consiglio

Staino

2010

Ann Oper Res

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Sovereign states issue fixed and floating securities to fund their public debt. The value of such portfolios strongly depends on the fluctuations of the term structure of interest rates. This is a typical example of planning under uncertainty, where decisions have to be taken on the base of the key stochastic economic factors underneath the model.We propose a multistage stochastic programming model to select portfolios of bonds, where the aim of the decision maker is to minimize the cost of the decision process. At the same time, we bound the conditional Value-at-Risk, a measure of risk which accounts for the losses of the tail distribution. We build an efficient frontier to trade-off the optimal cost versus the conditional Value-at-Risk and analyze the results obtained.

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“…This model is illustrated using debt issuance data of the Italian government. Other notable work in this area includes Bernaschi et al (2007), which provides results on the multivariate simulation of interest rates using observable (ECB) rates as well as analysis of principal components. The research reported in Consiglio and Staino (2010) and Balibek and Köksalan (2010) is the closest in spirit to the work reported here, in the sense that, both these papers also develop multi-stage stochastic programming models for sovereign debt issuance.…”

Section: The Debt Management Problemmentioning

confidence: 99%

“…Bernaschi et al (2007)), we do not use macroeconomic variables to model the evolution of interest rates. Our supporting argument is that, the secondary sovereign debt market for OECD countries is quite liquid and reflects the view of the market participants about the evolution of macroeconomic variables.…”

Section: Y(t T ) = − 1 T − T P (T T ) = Log(a(t T )) − B(t T )R Tmentioning

confidence: 99%

A mixed integer linear programming model for optimal sovereign debt issuance

Date

Canepa

Abdel-Jawad

2011

European Journal of Operational Research

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Governments borrow funds to finance the excess of cash payments or interest payments over receipts, usually by issuing fixed income debt and index-linked debt. The goal of this work is to propose a stochastic optimization-based approach to determine the composition of the portfolio issued over a series of government auctions for the fixed income debt, to minimize the cost of servicing debt while controlling risk and maintaining market liquidity. We show that this debt issuance problem can be modeled as a mixed integer linear programming problem with a receding horizon. The stochastic model for the interest rates is calibrated using a Kalman filter and the future interest rates are represented using a recombining trinomial lattice for the purpose of scenario-based optimization. The use of a latent factor interest rate model and a recombining lattice provides us with a realistic, yet very tractable scenario generator and allows us to do a multi-stage stochastic optimization involving integer variables on an ordinary desktop in a matter of seconds. This, in turn, facilitates frequent re-calibration of the interest rate model and re-optimization of the issuance throughout the budgetary year allows us to respond to the changes in the interest rate environment. We successfully demonstrate the utility of our approach by out-of-sample back-testing on the UK debt issuance data.

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Scenario-generation methods for an optimal public debt strategy

Cited by 15 publications

References 18 publications

Singular risk-neutral valuation equations

Singular risk-neutral valuation equations

A stochastic programming model for the optimal issuance of government bonds

A mixed integer linear programming model for optimal sovereign debt issuance

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