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

In recent years investment products have become more complex by providing investorswith various guarantees and bonus options. This increase in complexity hasprovided an impetus for the investigation into integrated asset and liability managementframeworks that could realistically address dynamic portfolio allocation in arisk-controlled way.This thesis presents two stochastic programming frameworks forthe asset and liabilitymanagement of investment products with guarantees. The asset side of theseproducts usually contains fixed income securities. For this reason we are concernedwith the stochastic evolution of the shape of the term structure of interest rates (oryield curve) over time. Literature in the field of scenario generation for multi-periodstochastic programs has stated that the generation of a set of scenarios, whichrepresents the uncertainty in the evolution of these risk factors over time, is oneof the most important and critical steps in the multi-stage stochastic programmingapproach. The first part of this thesis presents two methods for yield curve scenariogeneration. The first method uses a moment-matching approach and the seconda simulation approach which takes the movement of macro-economic factors intoaccount.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 stepssmaller than those at which portfolio rebalancing (or restructuring, i.e. changing theportfolio composition) takes place. The yield curve scenarios at these intermediatetime points have to be path dependent. Firstly this thesis proposes a momentmatchingapproach to construct scenario trees with path dependent intermediatediscrete yield curve outcomes sufficient for the pricing of fixed income securities.As part of the second approach we estimate an econometric model that fits theSouth African term structure of interest rates, using a Kalman filter approach. Theproposed model includes four latent factors and three observable macro-economic factors (capacity utilisation, inflation and repo-rate). The goal is to capture the dynamicinteractions between the macro-economy and the term structure. The resultingmodel can be used to generate interest rate scenario trees that are suitable forfixed income portfolio optimisation. An important input into our scenario generatoris the investor's view on the future evolution of the repo-rate. In practice most financialinstitutions have views on the macro-economy. These views are produced bymeans of an economic scenario generator (ESG) or expert opinion. These ESG'sonly produce forecasts for macro-economic factors, for example the repo-rate andnot 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 liquidasset portfolios found in the banking environment and the second problem is theasset and liability management of insurance products with minimum guarantees.We discuss the formulation and implementation of these mUlti-stage stochastic programmingmodels and back-test both models on real market data.Maintaining liquid asset portfolios involves a high carry cost and is mandatory bylaw for some financial institutions. Taking this into account, a financial institution'saim is to manage a liquid asset portfolio in an "optimal" way, such that it keepsthe minimum allowed liquid assets to comply with regulations. This thesis proposesa mUlti-stage dynamic stochastic programming model for liquid asset portfoliomanagement. The model allows for portfolio rebalancing decisions over a multiperiodhorizon, as well as for flexible risk management actions, such as reinvestingcoupons at intermediate time steps.The second problem is the asset and liability management of insurance productswith minimum guarantees. This thesis proposes a mUlti-stage dynamic stochasticprogramming model for the integrated asset and liability management of insuranceproducts with guarantees that minimise the down-side risk of these products. Weinvestigate with-profits guarantee funds by including regular bonus payments whilekeeping the optimisation problem linear. The main focus is the formulation andimplementation of a multi-stage stochastic programming model Dynamic optimization is perceived to be too difficult. .. It would be nice to have ageneric 'sledge hammer' approach for attacking this sort of problem. 1A. D. Smith (1996), p. 1085