Optimal Asset-Liability Management for Defned Beneft Pension Fund Under Stochastic Correlation

We consider a second pillar pension fund problem relying on a multi-stage stochastic asset-liability management (ALM) model which is specified with an asset universe including money-market, fixed-income, inflation-linked bond as well as equity and commodity. The current value of liability is determined under the assumptions of constant pension fund future pension payments and their current market value (current fund obligation) under assumption of constant pension fund population by discounting all future pension payments. Pension payments are random and determined by the evolution of the population and by inflation. Over a long-term horizon discount rates will also fluctuate and derive the evaluation of the fund liabilities. The pension manager will seek an optimal investment strategy to fund all liabilities and generate the surplus. We present an extension of a scenario tree generation procedure to include stochastic correlations among asset classes and test whether, as claimed by several authors, such extension is effective during crises periods, when correlation clustering is commonly claimed to affect the markets and reduce significantly the effectiveness of portfolio diversification. We test the sensitivity of the first-stage implementable decision to alternative assumptions on the returns’ correlations and their impact on the portfolio terminal distribution during a crisis period. The funding ratio (FR) is the ratio of the portfolio assets to the liabilities. A pension funds, primary aim is to assess the FR at every decision stage over time. The pension fund’s manager wishes to have sufficient liquidity and to control interest and inflation rate risks with a minimum return guarantee. Asset returns are defined with respect to a risk exposure captured by the concept of risk capital, recently introduced in modern pension systems and which is becoming a standard in Institutional ALM and in particular in pension fund ALM. In this thesis the elements of a real-world case problem are discuss and results presented over a 10-year horizon with the pension fund economic and financial constraints. Focusing on a period, between 2009-2011, of increasing markets’ volatility, we analyze the effectiveness of a long-term, discrete dynamic investment strategy under an assumption of stochastic correlation. The method relies on the definition of a probability space generated through Monte Carlo simulation and the implementation of a scenario generation scheme with a Dynamic Conditional Correlation (DCC) model. We consider a defied benefit (DB) pension fund problem: under a DB scheme benefits are defined in terms of percentage of last year salaries. The liability of pension fund is also called defined benefit obligation (DBO) under such assumption. stressed funding condition will arises when assets value decreases and liability value increase. The analysis of pension funds market perspectives is strictly related with evolution of the funding ratio. The collected evidence supports the inclusion of stochastic correlation between asset returns during the recent European financial crisis. Over a three year backtesting period which includes the 2009-2011 sovereign crisis, the introduced extension is shown to generate an effective hedge to positive risk premium.