Asset Liability Management Model Research Articles

Worst-case Conditional Value at Risk for asset liability management: A framework for general loss functions

Asset–liability management (ALM) is a challenging task faced by pension funds due to the uncertain nature of future asset returns, employees’ wages, and interest rates. To address this challenge, this paper presents a new mathematical model that uses a Worst-case Conditional Value-at-Risk (WCVaR) constraint to ensure that, with high probability, the funding ratio remains above a regulator-mandated threshold under the worst-case density function that plausibly explains historical sample data. A tractable reformulation of this WCVaR constraint is developed based on the definition of the Worst-case Lower Partial Moment (WLPM) for a general loss function. Additionally, a data-driven moment-based ambiguity set is constructed to capture uncertainty in the moments of the density functions of random variables in the ALM problem. The proposed approach is evaluated using real-world data from the Canada Pension Plan (CPP) and is shown to outperform classical ALM models, based on either CVaR or WCVaR with fixed moments, on out-of-sample data. The proposed framework for handling correlated uncertainty using WCVaR with nonlinear loss functions can be used in other application areas.

Development of a new asset liability Management model with liquidity and inflation risks based on the Lower Partial Moment

Inflation and liquidity risks are two significant risks with which pension fund managers must contend. This study develops a new multi-period Asset Liability Management model to address these challenges. The model objective function minimizes both risks simultaneously. The Lower Partial Moment measure is used to minimize investment portfolio risk and a CVaR constraint is employed to avoid loss. A hybrid ARIMA-GARCH model is developed to generate scenarios regarding a case study from Iran. To do so, four different investment cases out of seven stocks from the stock market, one bond, three foreign currencies (Dollar, Euro, and Yen) and gold are considered. Findings affirm model efficacy and the model suggests that a portfolio of all four assets is the best investment strategy.

A stochastic Asset Liability Management model for life insurance companies

We build a stochastic Asset Liability Management (ALM) model for a life insurance company. Therefore, we deal with both an asset portfolio, made up of bonds, equity and cash, and a liability portfolio, comprising with-profit life insurance policies. We define a mortality model and a surrender model, as well as a new production model. First, with the purpose of ensuring the solvency of the company and the achievement of a competitive return, in the interest of both shareholders and policyholders, the insurer’s portfolio is periodically rebalanced according to the solution of a nonlinearly constrained optimization problem that aims to match asset and liability durations, subject to the attainment of a target return. In addition, several real-world constraints are imposed. When computing the company balance sheet projections, we consider not only future maturity and death payments, but also future surrender payments and all the cash flows due to new production, in order to obtain estimates that are as reliable as possible. The estimation of the timing and of the numbers of future surrenders and of future new policyholders requires the approximation of conditional expectations: To this end, we employ the least squares Monte Carlo technique. Secondly, for each bonds asset class and for equity asset class we propose a sectorial optimization problem with the aim of maximizing the expected value of a chosen utility function, subject to the results obtained from the first stage of portfolio rebalancing. Finally, we analyze a case study.

Capital structure choices, pension fund allocation decisions and the rational pricing of liability streams

AbstractThis paper introduces an integrated asset-liability management model that allows for the joint quantitative analysis of capital structure choices, pension fund allocation decisions and rational pricing of liabilities. We confirm that capital structure decisions have a substantial impact on the value of pension claims, and we provide a quantitative assessment of the mispricing induced by the use of an arbitrary regulatory discount rate. We also present a quantitative assessment of the asset substitution effect implied by a change in the pension fund allocation to risky assets taking place after the corporate and pension obligation claims have been issued.

Long-Term Stability of a Life Insurer's Balance Sheet

In this paper we devise a general, stochastic asset-liability management model for life insurance companies, based on the work of Gerstner et al. (2008). While the basic concept and structure are similar, we expand their model and specify several aspects in greater detail. One of the main extensions is the incorporation of new business, i.e. the addition of newly concluded contracts and thus insured in each period. This leads to new results on the consistency of the balance sheet equations. We can then utilize these to analyze the long-term behavior and the stability of the components of the balance sheet for different asset-liability approaches. Furthermore, we explicitly address the problem of the efficient simulation of a given large insurance portfolio by proposing an approach for the generation of cohorts and the integration of new contracts.

A decision-dependent randomness stochastic program for asset–liability management model with a pricing decision

In this study, we present a stochastic programming asset–liability management model which deals with decision-dependent randomness. The model focuses on a pricing problem and the subsequent asset–liability management problem describing the typical life of a consumer loan. Such problems are frequently tackled by many companies, including multinationals. When doing so, they must consider numerous factors. These factors include the possibility of their customer rejecting the loan, the possibility of the customer defaulting on the loan and the possibility of prepayment. The randomness associated with these factors have a clear relationship with the offered interest rate of the loan which is the company’s decision and thus, induces decision-dependent randomness. Another important factor, which plays a major role for liabilities, is the price of money in the market. This is determined by the market interest rates. We captured their evolution in the form of a scenario tree. In summary, we formulated a non-linear, multi-stage stochastic program with decision-dependent randomness, which spanned the lifetime of a typical consumer loan. Its solution showed us the optimal decisions that the company should make. In addition, we performed a sensitivity analysis demonstrating the results of the model for various parameter settings that described different types of customers. Finally, we discuss the losses caused if companies do not act in the optimal way.

Asset liability management for Tanzania pension funds by stochastic programming

We present a long-termmodel of asset liability management for Tanzania pension funds. The pension system is pay-as-you-go where contributions are used to pay current benefits. The pension plan is a final salary defined benefit. Two kinds of pension benefits, a commuted (at retirement) and a monthly (old age) pension are considered. A decisive factor for a long-term asset liability management is that, Tanzania pension funds face an increase of their members’ life expectancy, which will cause the retirees to contributors dependence ratio to increase. We present a stochastic programming approach which allocates assets with the best return to raise the asset value closer to the level of liabilities. The model is based on work by Kouwenberg in 2001, with features from Tanzania pension system. In contrast to most asset liability management models for pension funds by stochastic programming, liabilities are modeled by using number of years of life expectancy for monthly benefit. Scenario trees are generated by using Monte Carlo simulation. Numerical results suggest that, in order to improve the long-term sustainability of the Tanzania pension fund system, it is necessary to make reforms concerning the contribution rate, investment guidelines and formulate target funding ratios to characterize the pension funds’ solvency situation. Keywords: Pay-as-you-go pension fund, asset liability management, stochastic programming, scenario trees. AMS 2010 Mathematics Subject Classification: 62P05, 90C15

Generalization of the Annuity Factor

The well-known Annuity Factor, restricted to constant payments only, can be generalized for time dependent payments. A Generalized Annuity Factor (GAF) broadens the application potential considerably as is shown exemplarily for the valuation of loans and pension obligations. For the first time for such linear and nonlinear payments over time, compressed closed-form formulae for important financial key numbers such as present value, duration, convexity or value at risk can be derived. Moreover, easy computation makes General Annuity Factors a useful valuation tool especially in the field of finance and accounting. As General Annuity Factors can be implemented as User Defined Functions in a spreadsheet program, calculations can also be done in smaller firms or public services. Because of its computational efficiency the new instrument is also suitable for far-sighted economical models such as Asset Liability Management models (ALM) or life-cycle valuation models concerning products or investments.

New Asset Liability Management Model with Decision Support System for Life Insurance Companies: Interface Design Issues for Database and Mathematical Models

We introduce a new asset liability management (ALM) model based on decision support system (DSS) for a life insurance firm. The DSS is based on multi-stage stochastic linear programming (SLP) with recourse for strategic planning. The model can be used with minimal knowledge of management sciences. The model maximises the expected value of total reserve (policy holders' reserve and shareholders' reserve) at the end of the time period of planning with constraints both on the asset and the liability side of the firm's balance sheet. We discuss issues related to DSS interface design, one to one correspondences between the SLP model and the database and the difficulty in multi stage DSS compared to two stage DSS. We also compare and contrast the similarities and differences with our earlier work on SLP based DSS for process industries.

New asset liability management model with decision support system for life insurance companies: interface design issues for database and mathematical models

New asset liability management model with decision support system for life insurance companies: interface design issues for database and mathematical models

A multistage stochastic programming asset-liability management model: an application to the Brazilian pension fund industry

This paper proposes a multistage stochastic programming approach for the asset-liability management of Brazilian pension funds. We generate asset price scenarios with stochastic differential equations—Geometric Brownian Motion model for stocks and Cox–Ingersoll–Ross model for fixed income securities. Intertemporal solvency regulatory rules for Brazilian pension funds are considered endogenously in the model and enforced with a combinatorial constraint. A VaR probabilistic constraint is incorporated to obtain a positive funding ratio at each time period with high probability. Our approach uses multiple trees to provide a representative characterization of the uncertainty and is not computationally prohibitive. We evaluate the insolvency probability under different initial funding ratios through extensive simulations. The study reveals that the likely decrease of interest rate premiums in the next years will force pension fund managers to significantly change their portfolio strategies. They will have to take more risk in order to deliver the cash flows required to cover the liabilities and satisfy the regulatory constraints.

Asset Liability Modelling and Pension Schemes: The Application of Robust Optimization to USS

This paper uses a novel numerical optimization technique - robust optimization - that is well suited to solving the asset-liability management (ALM) problem for pension schemes. It requires the estimation of fewer stochastic parameters, reduces estimation risk and adopts a prudent approach to asset allocation. This study is the first to apply it to a real-world pension scheme, and the first ALM model of a pension scheme to maximise the Sharpe ratio. We disaggregate pension liabilities into three components - active members, deferred members and pensioners, and transform the optimal asset allocation into the scheme’s projected contribution rate. The robust optimization model is extended to include liabilities and used to derive optimal investment policies for the Universities Superannuation Scheme (USS), benchmarked against the Sharpe and Tint, Bayes-Stein, and Black-Litterman models as well as the actual USS investment decisions. Over a 144 month out-of-sample period robust optimization is superior to the four benchmarks across 20 performance criteria, and has a remarkably stable asset allocation - essentially fix-mix. These conclusions are supported by six robustness checks

Asset–liability modelling and pension schemes: the application of robust optimization to USS

This paper uses a novel numerical optimization technique – robust optimization – that is well suited to solving the asset–liability management (ALM) problem for pension schemes. It requires the estimation of fewer stochastic parameters, reduces estimation risk and adopts a prudent approach to asset allocation. This study is the first to apply it to a real-world pension scheme, and the first ALM model of a pension scheme to maximize the Sharpe ratio. We disaggregate pension liabilities into three components – active members, deferred members and pensioners, and transform the optimal asset allocation into the scheme's projected contribution rate. The robust optimization model is extended to include liabilities and used to derive optimal investment policies for the Universities Superannuation Scheme (USS), benchmarked against the Sharpe and Tint, Bayes–Stein and Black–Litterman models as well as the actual USS investment decisions. Over a 144-month out-of-sample period, robust optimization is superior to the four benchmarks across 20 performance criteria and has a remarkably stable asset allocation – essentially fix-mix. These conclusions are supported by six robustness checks.

Macroeconomic Volatility in Emerging Countries: A Mean-Variance Asset-Liability Management Model

This paper studies a novel approach for managing macroeconomic volatility in commodity exporting countries. As part of this study, we develop a sovereign risk management model in the context of an Asset-Liability Management (ALM) framework. Our first contribution is an extension of the parsimonious Nijman and Swinkels (2008) pension fund model to a much broader macroeconomic setting using new data while developing unconditional investment allocation and optimal sovereign hedging policies for exporting countries. As the strategies are designed in the static mean-variance setting, the optimal solutions are contingent upon discrete-time realisations of deterministic return moments. However, preliminary investigation of the distributional properties of the data lend credence to the consensus view that the time-invariance assumption may be notoriously incorrect, warranting a relaxation of the restrictive assumptions and the application of advanced statistical procedures. Consequently, as a second contribution, we account for partial autocorrelation, significant heteroskedasticity, cointegration and non-linear dependence in the sample data by adopting GARCH and Error Correction models to enhance the forecasting accuracy of optimal hedge ratios. Thirdly, we propose overlay hedging strategies that, when used in conjunction with the portfolio results, guarantee Pareto efficient allocation. Furthermore, we document substantial increases in Sharpe ratios and significant reduction in Cornish-Fisher value-at-risk and maximum drawdowns. Our portfolio allocation and hedging results suggest buying commodity-linked instruments where the current sovereign market exposure in an endowment is lower than the model implied optimal quantity and selling the instruments where the actual quantity exported exceeds the optimal threshold.

A robust optimization approach to asset-liability management under time-varying investment opportunities

This paper presents an asset liability management model based on robust optimization techniques. The model explicitly takes into consideration the time-varying aspect of investment opportunities. The emphasis of the proposed approach is on computational tractability and practical appeal. Computational studies with real market data study the performance of robust-optimization-based strategies, and compare it to the performance of the classical stochastic programming approach.

Dynamic Optimal Pension Fund Portfolios when Risk Preferences Are Heterogeneous among Pension Participants

AbstractIn this paper, we consider the problem of an optimal pension fund portfolio given the heterogeneous risk preferences of pension fund participants. The relative risk aversion of a pension fund tends to be a decreasing function of the level of aggregate wealth. We find that the dynamic optimal portfolio is simply characterized as the weighted sum of the optimal portfolio for each participant. Our model helps successfully establish the microfoundation of asset liability management models. A numerical example using recent Japanese data indicates the significant total welfare losses of adopting a suboptimal portfolio strategy and an inefficient risk‐sharing rule.

Risk Decision Support System for Asset Liability Management

This paper outlines a risk decision support system designed to arrive at well-substantiated policy decisions using asset liability management (ALM) models. The risk decision support system explicitly takes into account that 1) there are multiple risk and return measures that are all important to some extent, 2) there are multiple stakeholders with different (and typically to some extent conflicting) objectives and 3) there is model uncertainty and therefore (economic) stress tests should also play a role in the decision making process. The method is based on techniques from the operations research literature on multicriteria decision making and group decision support to map outcomes generated by any ALM model into policy preferences of (the stakeholders of) the organization in question. Literature on robust control theory is used to guide us how to make good decisions when the ALM model is regarded as just an approximation to an unknown and unspecified model that actually generates the data. The risk decision support system can be used theoretically to obtain insight in for example the influence of a change in future regulation on policy choices or to help design future (pension) contracts. In pract ice experience learned us that the method facilitates discussions and decision making substantially since the approach helps parties to focus on interests (objectives), rather than positions (alternatives).

Collective adjustment of pension rights in ALM models

Collective adjustment of pension rights is a way to keep defined benefit systems tenable. In asset liability management (ALM) models presented in the literature these decisions are modeled both at the aggregate level of the liabilities as a whole and at a more detailed level. In this paper we compare the approximate aggregate approach to the accurate detailed approach for the average earnings scheme with conditional indexation. We prove that the aggregate approach leads to one-sided errors. Moreover, we show that for semi-realistic data these biases are considerable.

Indexation of Dutch pension rights in multistage recourse ALM models

Indexation (correction for inflation) of defined benefit pension rights is an important topic in the current pension debate fostered by the ageing of populations. In the Netherlands, pension funds need to formulate policies concerning indexation. We show how indexation decisions can be modelled adequately in multistage recourse asset liability management (ALM) models, which can be used for supporting the policy making. Moreover, for a stylized pension fund, we analyze the working of these indexation decisions in a numerical experiment.

Efficient deterministic numerical simulation of stochastic asset-liability management models in life insurance

New regulations, stronger competitions and more volatile capital markets have increased the demand for stochastic asset-liability management (ALM) models for insurance companies in recent years. The numerical simulation of such models is usually performed by Monte Carlo methods which suffer from a slow and erratic convergence, though. As alternatives to Monte Carlo simulation, we propose and investigate in this article the use of deterministic integration schemes, such as quasi-Monte Carlo and sparse grid quadrature methods. Numerical experiments with different ALM models for portfolios of participating life insurance products demonstrate that these deterministic methods often converge faster, are less erratic and produce more accurate results than Monte Carlo simulation even for small sample sizes and complex models if the methods are combined with adaptivity and dimension reduction techniques. In addition, we show by an analysis of variance (ANOVA) that ALM problems are often of very low effective dimension which provides a theoretical explanation for the success of the deterministic quadrature methods.