LAUSR

Abstract When a financial institution has a difficulty to close a position in an illiquid asset, a practical solution is to hedge the risk of the position with a related liquid asset. This may frequently occur in insurance institutions who diversify asset allocation by illiquid investment and face high transaction costs when try to close the illiquid asset position. A conventional approach constructs optimal hedging based on the correlation between the liquid and illiquid assets. We show, however, that ignoring the serial dependence through cointegration significantly reduces the hedging effectiveness. This paper investigates the time-consistent mean-variance optimal hedging using cointegration for the risk of a non-traded portfolio. Specifically, only the investment amount in the liquid asset is the control variable. The mathematical challenge stems on the derivation of the optimal equilibrium strategy when we have to deal with cointegration, illiquidity and time-inconsistency simultaneously. Using a stochastic differential game approach, we characterize the equilibrium hedging strategy from a system of partial differential equations that involves an HJB equation for the time-consistent problem with cointegration. Novel solutions to the equilibrium strategy and the efficient frontier are obtained in explicit closed-form formulas. The significance of cointegration in the corresponding hedging problem is evidenced with real empirical data.