A multi-period stochastic programming approach to integrated asset and liability management of investment products with guarantees / Helgard Raubenheimer

Abstract

In recent years investment products have become more complex by providing investors with various guarantees and bonus options. This increase in complexity has provided an impetus for the investigation into integrated asset and liability management frameworks that could realistically address dynamic portfolio allocation in a risk-controlled way. This thesis presents two stochastic programming frameworks forthe asset and liability management of investment products with guarantees. The asset side of these products usually contains fixed income securities. For this reason we are concerned with the stochastic evolution of the shape of the term structure of interest rates (or yield curve) over time. Literature in the field of scenario generation for multi-period stochastic programs has stated that the generation of a set of scenarios, which represents the uncertainty in the evolution of these risk factors over time, is one of the most important and critical steps in the multi-stage stochastic programming approach. The first part of this thesis presents two methods for yield curve scenario generation. The first method uses a moment-matching approach and the second a simulation approach which takes the movement of macro-economic factors into account. In asset and liability management under uncertainty, using stochastic programming, it is sometimes necessary to take into account flexible risk management actions, for example the reinvestment of coupons or the payment of liabilities at time steps smaller than those at which portfolio rebalancing (or restructuring, i.e. changing the portfolio composition) takes place. The yield curve scenarios at these intermediate time points have to be path dependent. Firstly this thesis proposes a momentmatching approach to construct scenario trees with path dependent intermediate discrete yield curve outcomes sufficient for the pricing of fixed income securities. As part of the second approach we estimate an econometric model that fits the South African term structure of interest rates, using a Kalman filter approach. The proposed model includes four latent factors and three observable macro-economic factors (capacity utilisation, inflation and repo-rate). The goal is to capture the dynamic interactions between the macro-economy and the term structure. The resulting model can be used to generate interest rate scenario trees that are suitable for fixed income portfolio optimisation. An important input into our scenario generator is the investor's view on the future evolution of the repo-rate. In practice most financial institutions have views on the macro-economy. These views are produced by means of an economic scenario generator (ESG) or expert opinion. These ESG's only produce forecasts for macro-economic factors, for example the repo-rate and not a complete yield curve. The second part of this thesis introduces and solves two asset and liability problems. The first problem is the asset and liability management of minimum liquid asset portfolios found in the banking environment and the second problem is the asset and liability management of insurance products with minimum guarantees. We discuss the formulation and implementation of these mUlti-stage stochastic programming models and back-test both models on real market data. Maintaining liquid asset portfolios involves a high carry cost and is mandatory by law for some financial institutions. Taking this into account, a financial institution's aim is to manage a liquid asset portfolio in an "optimal" way, such that it keeps the minimum allowed liquid assets to comply with regulations. This thesis proposes a mUlti-stage dynamic stochastic programming model for liquid asset portfolio management. The model allows for portfolio rebalancing decisions over a multiperiod horizon, as well as for flexible risk management actions, such as reinvesting coupons at intermediate time steps. The second problem is the asset and liability management of insurance products with minimum guarantees. This thesis proposes a mUlti-stage dynamic stochastic programming model for the integrated asset and liability management of insurance products with guarantees that minimise the down-side risk of these products. We investigate with-profits guarantee funds by including regular bonus payments while keeping the optimisation problem linear. The main focus is the formulation and implementation of a multi-stage stochastic programming model Dynamic optimization is perceived to be too difficult. .. It would be nice to have a generic 'sledge hammer' approach for attacking this sort of problem. 1 A. D. Smith (1996), p. 1085