Optimal Payoffs under State-dependent Preferences

Most decision theories, including expected utility theory, rank dependent utility theory and cumulative prospect theory, assume that investors are only interested in the distribution of returns and not in the states of the economy in which income is received. Optimal payoffs have their lowest outcomes when the economy is in a downturn, and this feature is often at odds with the needs of many investors. We introduce a framework for portfolio selection within which state-dependent preferences can be accommodated. Specifically, we assume that investors care about the distribution of final wealth and its interaction with some benchmark. In this context, we are able to characterize optimal payoffs in explicit form. Furthermore, we extend the classical expected utility optimization problem of Merton to the state-dependent situation. Some applications in security design are discussed in detail and we also solve some stochastic extensions of the target probability optimization problem

How valuable is your VaR? Large sample confidence intervals for normal VaR

http://henrystewart.metapress.com/app/home/contribution.asp?referrer=parent&backto=issue,7,8;searcharticlesresults,1,11;International audienceLittle is known about the distribution of the 'value-at-risk' (VaR) estimate and the associated estimation risk. In the case of the normal VaR, the key problem comes from the fact that it is estimated using a couple of parameters whose estimates are distributed differently. Previous research has either neglected uncertainty around the mean parameter, or resorted to simulations. By contrast, this paper derives analytical results for the normal VaR with the help of asymptotic theory and the so-called 'delta method'. Properties of the estimation errors are then explored in detail and the VaR estimation risk is broken down into its various components. It is then shown, among other things, that the fraction of error owing to mean uncertainty is limited in a prudential context. In other words, the approximate approach defended by Jorion and Chappell and Dowd is shown to still be relevant

On perpetual American strangles

International audienceThis paper analyzes perpetual American strangles with no recourse to advanced numerical techniques. Our analytical approach rests on an analogy with asymmetric rebates of Double Knock-Out Barrier Options. The optimal exercise policy is modelled by a couple of boundaries that simultaneously solve a system of two non linear equations. Numerical investigations then highlight salient features of American strangles and compare them with portfolios of options which may be used as proxies. Overall, results show that these latter are significantly upward biased in terms of prices and that, more dramatically, they lead the holder to exercise inappropriatel

A closed form solution for pricing defaultable bonds

International audienceCathcart and El-Jahel [Journal of Fixed Income 8 (1998)] have formalized the "signaling approach" for modeling the default risk of some risky bonds. Their pricing formula requires a numerical method to invert the Laplace transform of the default probability. This letter rather provides a closed form formula based on standard results of the theory of exotic barrier options. One verifies that the original numerical method implemented by Cathcart and El-Jahel [Journal of Fixed Income 8 (1998)] does not lead to significant computational errors

On Bankruptcy Procedures and the Valuation of Corporate Securities

International audienceThis paper extends the contingent claims analysis of Black-Scholes-Merton-Cox to account for the existence of a court-supervised bankruptcy procedure that is exclusively based on the time spent by the firm in distress. I provide some distribution-free results and analytical formulae that are very useful for pricing corporate securities. I highlight a number of price effects of the bankruptcy procedure and show, for instance, that thecredit spreads can decrease or increase with respect to the grace delay depending on the subordination feature of the corporate debt. Senior creditors should in turn worry about the effective enforceability of their safety covenant. Numerical experiments suggest that any effort to reinforce a safety covenant ex ante may be swept quite easily by a grace delay granted by a Court ex post. Finally, I discuss the portfolio management of corporate securities when portfolios are internationally diversified and I show how a portfolio manager can extend the initial one-country setting to amulti-country setting with different bankruptcy codes

René M. Stulz: latitude managériale et politique financière

International audienc

Continuous barrier range options

International audienceThis article presents a set of exotic barrier options whose appearance/ disappearance mechanism lies over a range of values. This family generalizes soft barrier options introduced by Hart and Ross and represents a simple alternative to steps options suggested by Linetsky Q2 for reducing knock-out risk. The traditional soft mechanism involves a uniformly distributed process. By contrast, Barrier Range Options use other density functions to account for more complex mechanisms