Abstracts

Pricing and hedging long dated liabilities faces two challenges. On one hand, the market for long maturity financial instrument is missing. The longest government bonds even in developed financial markets (such as US and Germany) has maturities no longer than 30 year. However, pension liabilities are well defined future cash flow obligations with more than 50 years of maturities. It is regulated by Solvency II that pension and insurance companies should follow a ``market-consistent'' principle to value their liabilities. Here comes the puzzle: how to implement ``market - consistent '' valuation on those commitments with maturities longer than 30 years; or how to discount the far future cash flows with the absence of a complete bond market?
On the other hand, extrapolating term structure model is exposed to parameter misspecification. Any valuation of a long dated liability with missing bond market must be model based. Conditional on a model, we could derive a term structure for all maturities. However, there are a large number of models that perfectly fit bond prices up to maturity of 30 years but yet imply different prices for the non-traded-period bonds.
Despite much work on the term structure models, very few studies consider the impact of model uncertainty on long dated liability valuation. In this paper, we propose a robust optimal hedging policy that minimize the hedging error of long dated liabilities in the presence of parameter uncertainty and missing bond market. Our replicating portfolio is robust to model misspecification in the sense that the investment policy is less sensitive to the choice of models.
We solve a dynamic robust optimization problem that maximin agent's utility. On one hand, agent allocates her instantaneous wealth between a short-term and a median-term bond market so as to minimize the expected shortfall of a long maturity commitment. On the other hand, Mother nature perturbs the estimate parameters in order to maximize the expected shortfall given the decision of the agent. The equilibrium portfolio is therefore, robust against model ambiguity. We use GMM approach to estimate the one-factor affine term structure model. Then we employ Least Square Monte Carlo method to solve the backward stochastic differential equation numerically.
We find that both naive and robust optimal portfolios depend on the hedging horizon and current funding ratio. The robust policy suggests to take more risk when the current funding ratio is low, but is another way around when funding ratio is sufficiently high. The robust yield curve derived through the minimum assets required to eliminate shortfall risk is lower than the naive one. For long-term investor, the robust policy is likely to outperform the naive one when bond premia is over estimated.