Pension Options Valuation and Hedging Bounds

In this paper, various option pricing models are used to provide analytical solutions to valuing defined pension liabilities (or securitised parts of pension liabilities) in incomplete markets. Unlike when markets are complete, there is not a single arbitrage-free price for liabilities but instead a range of prices consistent with the absence of arbitrage. We analyse and compare the application of incomplete market variants of the following models to pension liabilities: i) the standard Black-Scholes (1973) option model ii) the Margrabe (1978) exchange options model; iii) the Stulz (1982) rainbow option model to price pension schemes liabilities. No matter which approach is used, we find the range of liability prices to be broad, implying it is difficult to put a precise market value on pension liabilities. However, we also find that the implication for strategic asset allocation is relatively minimal; strategic asset allocations, at least in the models we looked at, appear to be relatively robust to incomplete markets. This conclusion is more about risk exposure than the financial instruments used to achieve a given level of risk exposure, as the desired financial instruments may depend considerably on the degree of market completeness.