Shortfall risk in long-term hedging with short-term futures contracts (Q2771114)

Forwards and futures seem to be ideal instruments for speculation or hedging against changes in the underlying asset price. If the future contract is market-to-market, however, large variation in asset prices may expose the investor to a cash shortfall. This would also arise for long term commitments hedged by short term forwards or futures. Here the cash shortfall risk up to the horizon \(k\leq N\), the running risk, as opposed to the risk at \(k\) -- the spot risk -- is analyzed for various hedging strategies. This is done for several discrete time single factor models of spot and futures prices. The models allow for reversion and have uncorrelated increases of variance \(\sigma^2\). The rolling stack hedging strategy, in which the number of short dated futures, decreases proportional to the terminal time, is studied in more detail. For tractability the discrete models are approximated by stochastic differential equations models. In this case the cash balance process \(A_t\) is Gaussian and the spot risk is described by \(\sigma_t^2 = \text{Var} (A_t)\), while the running risk is approximately given by \(v_t^2 =\sup_{0\leq s\leq t} \sigma_s^2\). More general and appropriate for this theory, however, is the method of large deviations, because it gives more information when and how a shortfall is going to occur. The key concept in this approach is the analysis of most likely paths for large deviations. This is applied to various models and hedging strategies. For comparison and assessment of the approximation simulations for the discrete model are also presented. The general pattern of all of this is that the riskiness of the full hedge versus no hedge decreases with the magnitude of the shortfall and the coefficient of reversion. The author also identifies superior hedging strategies.NEWLINENEWLINEFor the entire collection see [Zbl 0967.91001].