Pricing and Hedging Pension Fund Liability via Portfolio Replication

This thesis is composed by three works concerning multistage stochastic programming (MSP) applications for implementing optimal decisions for defined benefit pension funds into an asset and liability management framework. The first research focuses on the development of a method for generating asset returns scenario tree processes which serve as the input specification for the risky factors in the optimization MSP problem for general financial applications. In particular the proposed method produces a scenario tree for asset returns which does not contain arbitrage opportunities and which fits the first four moments of the reference probability distribution describing the uncertain nature of the risky factors. The second work deals with the problem of evaluating the liability of a defined benefit pension fund on a market based approach. The proposed methodology has been developed on a risk measure replication approach in a discrete time setting and solved with a numerical optimization approach via MSP. The approach needs the design of a statistical model for all the risky factors driving the pension fund asset and liability dynamic. The statistical model is then used to generate a discrete space and time representation of the risky factors dynamic by means of a scenario tree. The actual price of the pension fund liability will be then defined as the minimum initial capital in order to construct a self-financing trading strategy which replicates the future pensions net expenditure with a certain degree. The degree in which the replication is performed is evaluated on the basis of a risk measure. Finally we propose a methodology to price a longevity swap contract from the point of view of the pension fund manager as the third contribution. We have defined the swap price (the fixed rate) as the maximum fixed rate that allows the pension fund to enter the contract without worsening the liability present value obtained with the risk measure replication approach developed in the second work of this thesis.