0000000001252114
AUTHOR
Stavros A. Zenios
Designing Guarantee Options in Defined Contribution Pension Plans
The shift from defined benefit (DB) to defined contribution (DC) is pervasive among pension funds, due to demographic changes and macroeconomic pressures. In DB all risks are borne by the provider, while in plain vanilla DC all risks are borne by the beneficiary. For DC to provide income security some kind of guarantee is required. A minimum guarantee clause can be modeled as a put option written on some underlying reference portfolio of assets and we develop a discrete model that optimally selects the reference portfolio to minimise the cost of a guarantee. While the relation DB-DC is typically viewed as a binary one, the model can be used to price a wide range of guarantees creating a con…
A model for designing callable bonds and its solution using tabu search
Abstract We formulate the problem of designing callable bonds as a non-linear, global, optimization problem. The data of the model are obtained from simulations of holding-period returns of a given bond design, which are used to compute a certainty equivalent return, viz., some target assets. The design specifications of the callable bond are then adjusted so that the certainty equivalent return is maximized. The resulting problem is multi-modal, and a tabu search procedure, implemented on a distributed network of workstations, is used to optimize the bond design. The model is compared with the classical portfolio immunization model, and the tabu search solution technique is compared with s…
Risk Management for Sovereign Debt Financing with Sustainability Conditions
We develop a model of debt sustainability analysis with optimal financing decisions in the presence of macroeconomic, financial and fiscal uncertainty. We define a coherent measure of refinancing risk, and trade off the risks of debt stock and flow dynamics, subject to debt sustainability constraints and endogenous risk and term premia. We optimize both static and dynamic financing strategies, compare them with several simple rules and consol financing to demonstrate economically significant effects of optimal financing, and show that the stock-flow tradeoff can be critical for sustainability. We quantify the minimum refinancing risk and the maximum rate of debt reduction that a sovereign c…
Stochastic debt sustainability analysis for sovereigns and the scope for optimization modeling
We express the opinion that sovereign debt sustainability analysis must be augmented by stochastic correlated risk factors and a risk measure to capture tail effects. Crisis situations can thus be adequately specified and analyzed with sufficient accuracy to warrant the relevance of policy decisions. In this context there is significant scope for optimization modeling for both strategic planning and operational management. We discuss diverse aspects of the problem of debt sustainability and highlight modeling approaches that can be brought to bear on the problem. Results with the fictitiuous, but nor unrealistic, Kingdom of Atlantis, which is sinking under excessive debt, illustrate the pro…
The Case for Contingent Convertible Debt for Sovereigns
We make the case for sovereigns to issue contingent convertible bonds as a means to forestall debt crises. These instruments contractually stipulate payment standstill, contingent on a sovereign’s credit default swap spread breaching a distress threshold. This is a financial innovation solution to the lack of sovereign debt restructuring mechanisms, limiting ex ante the likelihood of debt crises and imposing ex post risk sharing between creditors and the debtor. The new instruments are contingent contracts addressing neglected risks in sovereign debt. Building on literature for contingent convertible debt for banks we address the design of sovereign contingent debt, including market discipl…
Designing and pricing guarantee options in defined contribution pension plans
Abstract The shift from defined benefit (DB) to defined contribution (DC) is pervasive among pension funds, due to demographic changes and macroeconomic pressures. In DB all risks are borne by the provider, while in plain vanilla DC all risks are borne by the beneficiary. However, for DC to provide income security some kind of guarantee is required. A minimum guarantee clause can be modeled as a put option written on some underlying reference portfolio and we develop a discrete model that selects the reference portfolio to minimize the cost of a guarantee. While the relation DB–DC is typically viewed as a binary one, the model shows how to price a wide range of guarantees creating a continu…
Risk management optimization for sovereign debt restructuring
Debt restructuring is one of the policy tools available for resolving sovereign debt crises and, while unorthodox, it is not uncommon. We propose a scenario analysis for debt sustainability and integrate it with scenario optimization for risk management in restructuring sovereign debt. The scenario dynamics of debt-to-GDP ratio are used to define a tail risk measure, termed "conditional Debt-at-Risk". A multi-period stochastic programming model minimizes the expected cost of debt financing subject to risk limits. It provides an operational model to handle significant aspects of debt restructuring: it collects all debt issues in a common framework, and can include contingent claims, multiple…
Pricing and Hedging GDP-Linked Bonds in Incomplete Markets
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 …
Integrated simulation and optimization models for tracking international fixed income indices
Portfolio managers in the international fixed income markets must address jointly the interest rate risk in each market and the exchange rate volatility across markets. This paper develops integrated simulation and optimization models that address these issues in a common framework. Monte Carlo simulation procedures generate jointly scenarios of interest and exchange rates and, thereby, scenarios of holding period returns of the available securities. The portfolio manager’s risk tolerance is incorporated either through a utility function or a (modified) mean absolute deviation function. The optimization models prescribe asset allocation weights among the different markets and also resolve b…
Asset and Liability Management for Insurance Products with Minimum Guarantees: The UK Case
Abstract Modern insurance products are becoming increasingly complex, offering various guarantees, surrender options and bonus provisions. A case in point are the with-profits insurance policies offered by UK insurers. While these policies have been offered in some form for centuries, in recent years their structure and management have become substantially more involved. The products are particularly complicated due to the wide discretion they afford insurers in determining the bonuses policyholders receive. In this paper, we study the problem of an insurance firm attempting to structure the portfolio underlying its with-profits fund. The resulting optimization problem, a non-linear program…
Insurance league: Italy vs. U.K
Insurers are competing by adopting product innovations that provide the insured with integrated coverage for actuarial and financial risks. This article compares the contract structures of blended life policies between the insurance markets in Italy and the United Kingdom within the context of asset-liability management and welfare analysis. © Emerald Backfiles 2007.
Pricing Sovereign Contingent Convertible Debt
We develop a pricing model for sovereign contingent convertible bonds (S-CoCo) with payment standstills triggered by a sovereign's credit default swap CDS spread. One innovation is the modeling of CDS spread regime switching which is prevalent during crises. Regime switching is modeled as a hidden Markov process and is integrated with a stochastic process of spread levels to obtain S-CoCo prices through simulation. The paper goes a step further and uses the pricing model in a Longstaff-Schwartz. American option pricing framework to compute state contingent S-CoCo prices at some risk horizon, thus facilitating risk management. Dual trigger pricing is also discussed using the idiosyncratic CD…
Pricing sovereign contingent convertible debt
We develop a pricing model for Sovereign Contingent Convertible bonds (S-CoCo) with payment standstills triggered by a sovereign's Credit Default Swap (CDS) spread. We model CDS spread regime switching, which is prevalent during crises, as a hidden Markov process, coupled with a mean-reverting stochastic process of spread levels under fixed regimes, in order to obtain S-CoCo prices through simulation. The paper uses the pricing model in a Longstaff-Schwartz American option pricing framework to compute future state contingent S-CoCo prices for risk management. Dual trigger pricing is also discussed using the idiosyncratic CDS spread for the sovereign debt together with a broad market index. …
Risk Management for Sovereign Financing within a Debt Sustainability Framework
The mix of instruments used to finance a sovereign is a key determinant of debt sustainability through its effect on funding costs and risks. We extend standard debt sustainability analysis to incorporate debt-financing decisions in the presence of macroeconomic, financial, and fiscal risks. We optimize the maturity of debt instruments to trade off borrowing costs with refinancing risk. Risk is quantified with a coherent measure of tail risk of financing needs, conditional Flow-at-Risk. A constraint on the pace of reduction of debt stocks is also imposed, and we model the effect of debt stocks on the yield curve through endogenous risk and term premia. On a simulated economy, we show that t…
Risk Profiles for Re-Profiling the Sovereign Debt of Crisis Countries
This paper uses a risk-management approach to re-profile the sovereign debt of countries facing debt crises. Using scenario analysis we develop a risk measure of the sovereign's debt -- Conditional Debt-at-Risk -- and an optimization model is used to trace risk profiles that tradeoff expected cost of debt financing against the Conditional Debt-at-Risk. The risk profiles are particularly informative for crisis countries, as they allow us to identify, with high-probability, debt unsustainability. We develop risk profiles for two Eurozone countries with excessive debt, Cyprus and Italy, both in their current form and under various forms of restructuring or rescheduling, and show how to assess …
The prometeia model for managing insurance policies with guarantees
Publisher Summary This chapter discusses the development of a scenario-based optimization model for asset and liability management for the participating policies with guarantees and bonus provisions offered by Italian insurers. The changing landscape of the financial services in Italy sets the backdrop for the development of this system which was the result of a multi-year collaborative effort between academic researchers, the research staff at Prometeia in Bologna, and end-users from diverse Italian insurers. It also presents and discusses the model and its key feature, and introduces several extensions. The resulting system allows the analysis of the tradeoffs facing an insurance firm in …
Risk Management Optimization for Sovereign Debt Restructuring
Abstract Debt restructuring is one of the policy tools available for resolving sovereign debt crises and, while unorthodox, it is not uncommon. We propose a scenario analysis for debt sustainability and integrate it with scenario optimization for risk management in restructuring sovereign debt. The scenario dynamics of debt-to-GDP ratio are used to define a tail risk measure, termed conditional Debt-at-Risk. A multi-period stochastic programming model minimizes the expected cost of debt financing subject to risk limits. It provides an operational model to handle significant aspects of debt restructuring: it collects all debt issues in a common framework, and can include contingent claims, m…
A Conditional Value–at–Risk Model for Insurance Products with Guarantee
We propose a model to select the optimal portfolio which underlies insurance policies with a guarantee. The objective function is defined in order to minimise the conditional value at-risk (CVaR) of the distribution of the losses with respect to a target return. We add operational and regulatory constraints to make the model as flexible as possible when used for real applications. We show that the integration of the asset and liability side yields superior performances with respect to naive fixed-mix portfolios and asset based strategies. We validate the model on out-of-sample scenarios and provide insights on policy design.
Portfolio diversification in the sovereign credit swap markets
We develop models for portfolio diversification in the sovereign credit default swaps (CDS) markets and show that, despite literature findings that sovereign CDS spreads are affected by global factors, there is sufficient idiosyncratic risk to be diversified. However, we identify regime switching in the times series of CDS spreads and spread returns, and the optimal diversified strategies can be regime dependent. The developed models trade off the CVaR risk measure against expected return, consistently with the statistical properties of spreads. We consider three investment strategies suited for different CDS market participants: for investors with long positions, speculators that hold unco…
Stochastic debt sustainability analysis for sovereigns and the scope for optimization modeling
We argue that sovereign debt sustainability analysis must be augmented by stochastic correlated risk factors and a risk measure to capture tail effects. Crisis situations can thus be adequately specified and analyzed with sufficient accuracy to warrant the relevance of policy decisions. In this context there is significant scope for optimization modeling for both strategic planning and operational management. We discuss diverse aspects of the problem of debt sustainability and highlight modeling approaches that can be brought to bear on the problem. Results with the fictitious, but nor unrealistic, Kingdom of Atlantis, which is sinking under excessive debt, illustrate the proposed models.
Pricing and hedging GDP-linked bonds in incomplete markets
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 byproduct 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. F…
Contingent convertible bonds for sovereign debt risk management
We consider convertible bonds that contractually stipulate payment standstill, contingent on a market indicator of a sovereign's creditworthiness breaching a distress threshold. This financial innovation limits ex-ante the likelihood of debt crises and imposes ex-post risk sharing between creditors and the debtor. Drawing from literature on contingent contracts, neglected risks, and bank CoCo, we extend prevailing arguments in favor of sovereign CoCo (S-CoCo). We discuss issues relating to their design: which market trigger, market discipline and sovereign incentives, and errors of false alarms or missed crises, and provide supporting evidence with eurozone data and a simple simulation on t…
Auditing Public Debt Using Risk Management
The Audit Office of the Republic of Cyprus conducted the first-ever audit of the country’s public debt, seeking answers to two key questions. Is government debt sustainable, and is debt financing efficient and effective in securing the lowest cost with acceptable risks? The audit’s findings were discussed by the parliament and can have significant ramifications for public finance. However, public debt management is quite complex, and the International Organization of Supreme Audit Institutions suggests that sufficient technical knowledge is essential in undertaking an audit, including an understanding of the uncertain macroeconomy, financing conditions, and government fiscal stance. We use…
Risk Management for Sustainable Sovereign Debt Financing
We model sovereign debt sustainability with optimal financing decisions under macroeconomic, financial, and fiscal uncertainty, with endogenous risk and term premia. Using a coherent risk measure we trade-off debt stock and flow risks subject to sustainability constraints. We optimize static and dynamic financing strategies and demonstrate economically significant savings from optimal financing compared with simple rules and consols, and find that optimizing the trade-offs can be critical for sustainability. The model quantifies minimum refinancing risk and maximum rate of debt reduction that a sovereign can achieve given its economic fundamentals, and an extension identifies optimal timing…
Designing portfolios of financial products via integrated simulation and optimization models
We analyze the problem of debt issuance through the sale of innovative financial products. The problem is broken down to questions of designing the financial products, specifying the debt structure with the amount issued in each product, and determining an optimal level of financial leverage. We formulate a hierarchical optimization model to integrate these three issues and provide constructive answers. Input data for the models are obtained from Monte Carlo simulation procedures that generate scenarios of holding period returns of the designed products. The hierarchical optimization model is specialized for the problem of issuing a portfolio of callable bonds to fund mortgage assets. The …
A parsimonious model for generating arbitrage-free scenario trees
Simulation models of economic, financial and business risk factors are widely used to assess risks and support decision-making. Extensive literature on scenario generation methods aims at describing some underlying stochastic processes with the least number of scenarios to overcome the ‘curse of dimensionality’. There is, however, an important requirement that is usually overlooked when one departs from the application domain of security pricing: the no-arbitrage condition. We formulate a moment matching model to generate multi-factor scenario trees for stochastic optimization satisfying no-arbitrage restrictions with a minimal number of scenarios and without any distributional assumptions.…
www.Personal_Asset_Allocation.
Today consumers demand delivery of financial services anytime and anywhere, and their needs and desires are evolving rapidly. The World Wide Web provides a rich channel for distributing customized services to a range of clients. An Internet-based system developed by Prometeia S.r.l. for Italian banks—both traditional and e-banks—supports consumers and financial advisors in planning personal finances. The system provides advice on allocating personal assets to fund consumers' needs, such as paying for a house, children's education, retirement, or other projects. State-of-the-art models of financial engineering—based on scenario optimization—develop plans that are consistent with clients' go…
Contingent Convertible Bonds for Sovereign Debt Risk Management
Abstract We consider convertible bonds that contractually stipulate payment standstill, contingent on a market indicator of a sovereign’s credit worthiness breaching a distress threshold. This financial innovation limits ex ante the likelihood of debt crises and imposes ex post risk sharing between creditors and the debtor. Drawing from literature on contingent contracts, neglected risks, and bank CoCo, we extend prevailing arguments in favor of sovereign CoCo (S-CoCo). We discuss issues relating to their design: which market trigger, market discipline and sovereign incentives, and errors of false alarms or missed crises, and provide supporting evidence with eurozone data and a simple simul…
The value of integrative risk management for insurance products with guarantees
Insurance liabilities are converging with capital markets products (e.g. derivatives and securitizations), thereby increasing the demand for integrated asset and liability management strategies. This article compares the value-added by an integrative approach-based on scenario optimization modelling-relative to traditional risk management methods. The authors present some examples of products offered by the insurance industry in Italy, and apply the results of the analysis to the design of competitive insurance policies. © Emerald Backfiles 2007.
Generating Multi-Asset Arbitrage-Free Scenario Trees with Global Optimization
Simulation models of economic, financial and business risk factors are widely used to assess risks and support decision-making. Extensive literature on scenario generation methods aims at describing some underlying stochastic processes with the least number of scenarios to overcome the "curse of dimensionality". There is, however, an important requirement that is usually overlooked when one departs from the application domain of security pricing: the no-arbitrage condition. We formulate a moment matching model to generate multi-factor scenario trees satisfying no-arbitrage restrictions with a minimal number of scenarios and without any distributional assumptions. The resulting global optimi…
Scenario optimization asset and liability modelling for individual investors
We develop a scenario optimization model for asset and liability management of individual investors. The individual has a given level of initial wealth and a target goal to be reached within some time horizon. The individual must determine an asset allocation strategy so that the portfolio growth rate will be sufficient to reach the target. A scenario optimization model is formulated which maximizes the upside potential of the portfolio, with limits on the downside risk. Both upside and downside are measured vis- `a-vis the goal. The stochastic behavior of asset returns is captured through bootstrap simulation, and the simulation is embedded in the model to determine the optimal portfolio. …
Asset and Liability Modelling for Participating Policies with Guarantee
We study the problem of asset and liability management of participating insurance policies with guarantees. We develop a scenario optimization model for integrative asset and liability management, analyze the tradeoffs in structuring such policies, and study alternative choices in funding them. The nonlinearly constrained optimization model can be linearized through closed form solutions of the dynamic equations. Thus large-scale problems are solved with standard methods. We report on an empirical analysis of policies offered by Italian insurers. The optimized model results are in general agreement with current industry practices. However, some inefficiencies are identified and potential im…