This paper examines the absolute and relative robustness of two of the most common methods for estimating implied probability density functions (PDFs) – the double-lognormal approximating function and the smoothed implied volatility smile methods – using short sterling futures options and the FTSE 100 index options. The changes resulting from randomly perturbing quoted prices by no more than a half tick provide a lower bound on the confidence intervals of the summary statistics derived from the estimated PDFs. Our tests show that the smoothed implied volatility smile method dominates the double lognormal as a technique for estimating implied PDFs.

Abstract Market discipline is an article of faith among financial economists, and the use of market discipline as a regulatory tool is gaining credibility. Effective market discipline involves two distinct components: security holders' ability to accurately assess the condition of a firm (monitoring) and their ability to cause subsequent managerial actions to reflect those assessments (influence). Substantial evidence supports the existence of market monitoring. However, the existing evidence about market influence involves relatively rare events such as management turnover. This paper seeks evidence that U.S. bank holding companies' security price changes reliably influence subsequent managerial actions. Although we identify some patterns consistent with beneficial market influences, our methodology does not provide strong evidence that stock or (especially) bond investors regularly influence managerial actions. Day-to-day market influence remains, for the moment, more a matter of faith than of empirical evidence. JEL classification codes: G21, G38, G14