Explicit formulas for optimal hedging stratergies for European contingent claims

In this paper, we consider the problem of discrete-time optimal hedging for a portfolio of (illiquid) European contingent claims (ECCs) written on multiple underlying assets. First, we present a framework to find discrete-time hedging strategies that minimize the variance of terminal wealth using a hedging portfolio of liquid assets, also assumed to ECCs written on the same underlying assets. Next, we specialize the framework to the case of illiquid portfolio consisting of a simple ECC written on a single underlying asset and a hedging portfolio consisting of the underlying asset and another simple ECC written on the same underlying asset. For this special case, we provide a (computable) formula for the minimum variance hedging strategy. Finally, we show that the minimum variance hedging strategy converges to the Δ-Γ-neutral hedging strategy as the interspacing between the hedging times converge to zero.