In this article, we analyze the impact of risk aversion on the valuation of defaultable bonds, and a simple multi-name credit derivative. Our approach is to work within intensity-based models, as initiated by, among others, Artzner and Delbaen, Madan and Unal, Lando and Jarrow and Turnbull. However, rather than pricing using no arbitrage arguments, we study the utility-indifference valuation mechanism, which entails analysis of portfolio optimization problems under default risk.
A major limitation of many traditional approaches is the inability to capture and explain high premiums observed in credit derivatives markets for unlikely events, for example the spreads quoted for senior tranches of CDOs written on investment grade firms. The approach explored here, and in our related work [28], aims to explain such phenomena as a consequence of tranche holders’ risk aversion, and to quantify this through the mechanism of utility indifference valuation.
One of the most important factors affecting the fitness of insect herbivores is their diet that is, the quality of the plant species they eat. Polyphagous herbivores in particular face a challenge, as eating different host plant species can result in differences in life-history traits, such as growth, development time and fecundity. These differences may be due to them having a limited possibility to co-evolve with all of their potential host plants, which have differing chemical (nutritional value, secondary metabolites) and other traits (e.g. mechanical defence) that affect the herbivores’life-history traits (Gordon, 1961; Erickson and Feeny, 1974; Cates, 1980; Price et al., 1980; Berenbaum and Zangerl, 1999). Thus, it is likely that generalist herbivores are adapted to the most common secondary metabolites and are more sensitive to defensive compounds that only occur in some plant genera (e.g. Levins and McArthur, 1966). However, plant secondary metabolites are not always harmful to herbivores; some of them are used as feeding cues, especially by specialist herbivores, and some can be beneficial to the herbivore. Carotenoids, for example, are important antioxidants and reduce the harmful effects of stress caused by, for example, ultraviolet radiation or infection (Demming-Adams and Adams, 1996; Ouchane et al., 1997).
It has often been demonstrated that generalist herbivores perform differently on different host plant species (e.g. Price et al., 1980; Bernays and Chapman, 1994). In spite of the performance differences, genetic interactions in the performance of herbivores feeding on different host plants have generally not been found (see, for example, Jaenike, 1990 and references therein). Genetic interactions in herbivores’ growth or other general performance measures on different host plant species would suggest that there is a trade-off in the metabolism of allelochemicals between different host plant species. The absence of these interactions has been interpreted to mean that the ‘metabolic load’ of detoxifying capacity (which is expected to be energy limited) has by itself a trivial effect on larvae (Scriber and Feeny, 1979; Appel and Martin, 1992). Looking for energy costs is perhaps not the best way to seek to understand the feeding costs of herbivores on many different host plant species.
Payday lending is a controversial segment of the consumer finance industry. A payday loan is a small, single payment loan that is repayable on the borrower’s next payday. Typically, payday loans are between $100 and $500 and have a term to maturity of about 14 days. Because of the small loan amount and short term to maturity, annual percentage rates for payday loans are commonly between 390 and 700 percent. Not surprisingly, the high annual percentage rates have led to allegations that payday loans are predatory. Industry critics often argue that the high interest charges and single payment feature of the product make repayment of the debt difficult, trapping many borrowers in a series of renewals that ultimately lead to insolvency. Payday lenders contend that the product satisfies credit constrained consumers’ liquidity needs for short term credit to manage unexpected expenses and shortfalls in cash. Although payday loans have a high price, the costs arising from delinquencies and late payments that such unexpected events could trigger may be even higher. These contentions need not be mutually exclusive. As with other credit products, some borrowers may have problems repaying while others are able to pay on time and receive benefits from the item being financed.
Historically, consumer finance companies provided small loans to relatively high risk, credit constrained consumers. Finance companies have largely abandoned the small loan market (Brito and Hartley 1995). Finance companies along with banks and credit unions prefer to provide access to such credit to more creditworthy consumers through revolving accounts. A notable characteristic that distinguishes payday loan customers from customers of other high price lenders such as pawnbrokers and rent to own companies is that all payday loan customers have a banking relationship. Payday loan customers must have a checking account to qualify for a payday loan, and most have an automobile loan or other type of consumer debt with a bank or finance company.
