When the underlying price process is a one‐dimensional diffusion, as well as in certain restricted stochastic volatility settings, a contingent claim's delta is bounded by the infimum and supremum of its delta at maturity. Further, if the claim's payoff is convex (concave), the claim's price is a convex (concave) function of the underlying asset's value. However, when volatility is less specialized, or when the underlying process is discontinuous or non‐Markovian, a call's price can be a decreasing, concave function of the underlying price over some range, increasing with the passage of time, and decreasing in the level of interest rates.

We investigate the effects of managerial outsourcing on the performance and incentives of mutual funds. Fund families outsource the management of a large fraction of their funds to advisory firms. These funds underperform those run internally by about 52 basis points per year. After instrumenting for a fund's outsourcing status, the estimated underperformance is three times larger. We hypothesize that contractual externalities due to firm boundaries make it difficult to extract performance from an outsourced relationship. Consistent with this view, outsourced funds face higher powered incentives; they are more likely to be closed after poor performance and excessive risk‐taking.

We examine the long‐standing question of whether firms derive value from investment bank relationships by studying how the Lehman collapse affected industrial firms that received underwriting, advisory, analyst, and market‐making services from Lehman. Equity underwriting clients experienced an abnormal return of around −5%, on average, in the 7 days surrounding Lehman's bankruptcy, amounting to $23 billion in aggregate risk‐adjusted losses. Losses were especially severe for companies that had stronger and broader security underwriting relationships with Lehman or were smaller, younger, and more financially constrained. Other client groups were not adversely affected.

Motivated by extant finance theory predicting that insider trading crowds out private information acquisition by outsiders, we use data for 100 countries for the years 1987–2000 to study whether analyst following in a country increases following restriction of insider trading activities. We document that analyst following increases after initial enforcement of insider trading laws. This increase is concentrated in emerging market countries, but is smaller if the country has previously liberalized its capital market. We also find that analyst following responds less intensely to initial enforcement when a country has a preexisting portfolio of strong investor protections.

We examine the expiration of the IPO quiet period, which occurs after the 25th calendar day following the offering. For IPOs during 1996 to 2000, we find that analyst coverage is initiated immediately for 76 percent of these firms, almost always with a favorable rating. Initiated firms experience a five‐day abnormal return of 4.1 percent versus 0.1 percent for firms with no coverage. The abnormal returns are concentrated in the days just before the quiet period expires. Abnormal returns are much larger when coverage is initiated by multiple analysts. It does not matter whether a recommendation comes from the lead underwriter or not.

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