The Journal of Finance

Option Prices and the Underlying Asset's Return Distribution

Published: 07/01/1991   |   DOI: 10.1111/j.1540-6261.1991.tb03776.x

BRUCE D. GRUNDY

This work examines the relation between option prices and the true, as opposed to risk‐neutral, distribution of the underlying asset. If the underlying asset follows a diffusion with an instantaneous expected return at least as large as the instantaneous risk‐free rate, observed option prices can be used to place bounds on the moments of the true distribution. An illustration of the paper's results is provided by the analysis of the information concerning the mean and standard deviation of market returns contained in the prices of S&P 100 Index Options.

Merton H. Miller: His Contribution to Financial Economics

Published: 12/17/2002   |   DOI: 10.1111/0022-1082.00364

Bruce D. Grundy

Merton Miller's status as a father of finance reflects the academic depth, breadth, and rigor of his writings and two important facets of his character. Merton was a man of great warmth and humor. He communicated his often challenging views via memorable phrases and anecdotes that have become part of the everyday language of the profession. Merton was also a man of great dedication. The whole profession has benefited from his devotion to his doctoral students, to his colleagues, and to his coauthors. This essay demonstrates how Merton's admiration for markets provided the foundation for all his research.

Disappearing Call Delay and Dividend‐Protected Convertible Bonds

Published: 10/13/2015   |   DOI: 10.1111/jofi.12363

BRUCE D. GRUNDY, PATRICK VERWIJMEREN

Firms do not historically call their convertible bonds as soon as conversion can be forced. A number of explanations for the delay rely on the size of the dividends that bondholders forgo so long as they do not convert. We investigate an important change in convertible security design, namely, dividend protection of convertible bond issues. Dividend protection means that the conversion value of the convertible bond is unaffected by dividend payments and thus dividend‐related rationales for call delay become moot. We document that call delay is near zero for dividend‐protected convertible bonds.

General Properties of Option Prices

Published: 12/01/1996   |   DOI: 10.1111/j.1540-6261.1996.tb05218.x

YAACOV Z. BERGMAN, BRUCE D. GRUNDY, ZVI WIENER

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.