Valuation of index-linked assets in incomplete markets

This proposal focuses on the valuation of pension contracts with conditional indexation in incomplete markets, recognizing the absence of perfect hedging instruments. A major issue in the discussion on pension reforms is the valuation of the entitlements of pension fund participants, whereby pension funds aim at providing inflation-protected benefits, but can only do so under a restrictive nominal supervisory framework and conditional on a favorable financial situation. Since Dutch inflation swaps are not traded on public markets, traditional valuation methods cannot be used to value Dutch inflation risks and, hence, a perfect hedge cannot be constructed. Hence, valuation becomes dependent on the risk appetite of the investor. This is particularly important for pension funds, because the risk appetite likely varies with the demography of the pension fund’s membership. Also their consumption basket differs from that of the average population member (e.g., elderly feature relatively high health care consumption). While there exists foreign indexed debt that could go some way towards protecting the purchasing power of pensions, this would still leave pension fund participants exposed to (real) exchange rate risk.
Similar valuation problems have been explored in the context of so-called real options using Stochastic Dynamic programming (SDP) to solve the valuation of risky cash flows as a function of the investor’s risk appetite (“utility indifference pricing”). The difficulty of applying these SDP techniques to higher dimensionality problems, such as those that arise in valuing long-dated pension fund liabilities, has long limited their practically use. This has changed with the recent development of highlyaccurate numerical approximation methods (for example, the “Least Squares Monte Carlo” method). We plan to apply them to pension plan evaluation in the presence of multiple sources of risks, of which some may be hedgeable and others not.

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