Abstract
This paper considers the multiperiod hedging decision in a framework of mean-reverting spot prices and unbiased futures markets. The task is to determine the optimal hedging path, i.e., the sequence of positions in futures contracts with the objective of minimizing the variance of an uncertain future cash flow. The model is used to illustrate both hedging using a matchedmaturity futures contract and hedging by rolling over a series of nearby futures contracts. In each case, the paper derives the conditions under which a single period (myopic) strategy would be optimal as opposed to a dynamic multiperiod strategy. The results suggest that greater the market power of the hedging entity, closer the optimal strategy is to a myopic hedge. The paper also highlights the difference in the optimal hedging path when hedging is based on matched-maturity as opposed to nearby contracts.
Highlights
Consider the hedging problem of a firm facing an uncertain future cash flow at a certain future time, T
The current study extends the analysis by explicitly allowing for mean reversion in the price process of the underlying of the futures contract as well
It is seen that if hedging is based on matched-maturity contracts, the optimal hedging strategy depends not so much on the absolute mean reversion rate of the hedged process, but rather on the relative mean reversion rates of the hedged and hedging processes
Summary
Consider the hedging problem of a firm facing an uncertain future cash flow at a certain future time, T. The current study extends the analysis by explicitly allowing for mean reversion in the price process of the underlying of the futures contract as well (referred to as the “hedging process”) In this extended framework, the HD model may be viewed as a special case in which hedging is carried out by rolling over a series of nearby contracts (“stack and roll” hedging, or just “stack” hedging). Their paper deals with the same problem of hedging a fixed cash position in the presence of basis risk They show that provided futures prices evolve as a martingale, it is possible to derive an optimal dynamic hedging strategy that is independent of risk preferences under fairly general assumptions about the relationship between spot and futures prices. The section contains a review of the literature, the following section develops the model and discusses implications and the final section concludes with a brief summary of the main results
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