Optimal Strategies For Hedging Basis Risk

Michael Monoyios (Brunel University)

The performance of optimal strategies for hedging a claim on a non-traded asset is analyzed. The claim is valued and hedged in a utility maximization framework, using exponential utility, with asset prices as lognormal diffusions. A traded asset, correlated with that underlying the claim, is used for hedging. Using a distortion method, an expectation representation for the claim's ask price is derived, in terms of the cumulant generating function of the terminal payoff. A formula for the optimal hedging strategy is also obtained. These lead to perturbation expansions for the price and hedging strategy, with terms in the expansions proportional to central moments of the claim payoff under the minimal martingale measure. The resulting fast computation capability is used to carry out a simulation based test of the optimal hedging program, computing the terminal hedging error from dynamic strategies over many asset price paths. These errors are compared with those from a naive strategy which uses the traded asset as a proxy for the non-traded one. The distribution of the hedging error acts as a suitable metric to analyze hedging performance. The optimal policy is found to improve hedging performance, with the hedging error distribution more sharply peaked around a non-negative profit. The frequency of profits over losses is increased, and this is measured by the median of the distribution, which is always increasedby the optimal strategies.