Exchange traded futures contracts often are not written on the specific asset that is a source of risk to a firm. The firm may attempt to manage this risk using futures contracts written on a related asset. This cross hedge exposes the firm to a new risk, the spread between the asset underlying the futures contract and the asset that the firm wants to hedge. Using the specific case of the airline industry as motivation, we derive the minimum variance cross hedge assuming a twofactor diffusion model for the underlying asset and a stochastic, mean-reverting spread. The result is a time-varying hedge ratio that can be applied to any hedging horizon. We also consider the effect of jumps in the underlying asset. We use
This paper discusses a practical case application of real options applied to license valuation in the aerospace maintenance, repair, and overhaul industry. After categorizing the available licensing opportunities of the firm, four distinct licensing classes are identified: traditional delay licenses, contingent investment licenses, licenses with cost uncertainties, and indefinite delay licenses. Due to the varying nature of the classes, accepted real option valuation techniques are applied to include the European call, dual asset, exchange, and perpetual option. Appropriate sensitivity analyses and discussion for each license class provide guidelines for decision‐making. In general, it is shown that the real options framework captures value overlooked by discounted cash flow approaches.
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