Recent models on optimal hedging investigate the hedging behavior for firms in incomplete markets in which there exist unhedgeable sources of background risk. Briys, Crouhy and Schlesinger (1993) and Mahul (2002) examine how the presence of basis risk alters the optimal hedging strategy in financial markets. Moschini and Lapan (1995) study the optimal hedging decisions for firms facing price, basis and production risk, assuming that hedging instruments are only available for price risk. Wong (2003a) investigates the optimal hedging decision of a competitive exporting firm which faces hedgeable exchange rate risk and non hedgeable price risk.
These models traditionally assume that contracts have no counter-party risk, also called credit risk; the counter-party is always assumed to make in full the promised payment. However, Johnson and Stulz (1985) notice that many financial assets are sold by investors that have limited assets and, therefore, default is often a possibility that must be taken seriously. Financial contracts exposed to credit risk are labeled “vulnerable contracts”. This source of risk is particularly relevant on the over-the-counter markets where no clearance board guarantees the full payment should the counter-party become insolvent. Several methods for pricing derivatives involving credit risk have been provided (see, for example, Johnson and Stulz 1987, Jarrow and Turnbull 1995) but, to our knowledge, the question concerning their proper application as a hedging instrument remains largely unexplored.
This paper examines the problem of a firm choosing an optimal hedge against price risk in financial markets where contracts are subject to unhedgeable/uninsurable credit risk. Its purpose is twofold. First, we investigate the firm’s hedging and production decisions when vulnerable forward contracts are available. The second purpose is related to the scant literature on the hedging role of options. This literature points out that options, in additions to futures, are an important hedging instrument when profits are not linear in the hedgeable source of risk. This non-linearity may stem from the production flexibility of the competitive firm (Moschini ad Lapan 1992, Wong 2003b) or the multiplicative interaction between the hedgeable and non-hedgeable risks (Sakong et al. 1993, Moschini and Lapan 1995, Brown and Toft 2001, Wong 2003a).
One of the main result of our paper is to offer another rationale for the hedging role of options traded on the over-the-counter markets. We show that the presence of credit risk induces the firm to purchase (vulnerable) options, even if these contracts are sold at a fair price and the profit function is linear in the hedgeable price risk. This contrasts with the previous studies that focus on the non-linearity of the profit function as the key point for the use of options. In addition, we show that the firm will only use (vulnerable) options and, therefore, (vulnerable) forward contracts are redundant.
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Hedging with Vulnerable Contracts
