Firms with high levels of organization capital (OK), a firm-specific production factor provided by key employees, are known to be risky and earn high stock returns. We argue that fragility of OK (i.e., its sensitivity to potential disruptions) is an independently important dimension of this risk. We proxy for fragility by the size of the top management team and show that firms with small teams outperform firms with big teams by 5% annually. The return spread increases in the level of OK and correlates with the outside options of top executives. Further supporting our interpretation, shocks to team composition from unexpected deaths of chief executive officers cause larger value losses in smaller teams.

Exceptional accuracy and speed for option pricing are available via quadrature (Andricopoulos, Widdicks, Duck, and Newton, 2003), extending into multiple dimensions with complex path-dependency and early exercise (Andricopoulos, Widdicks, Newton, and Duck, 2007). However, the exposition is incomplete, leaving many modelling processes outside the Black-Scholes-Merton framework unattainable. We show how to remove the remaining major block to universal application. Although this had appeared highly problematic, the solution turns out to be conceptually simple and implementation is straightforward (we provide code on the Journal of Financial Economics website at http://jfe.rochester.edu). Crucially, the method retains its speed and flexibility across complex combinations of option features but is now applicable across other underlying processes.

The exposition of the quadrature (QUAD) method (Andricopoulos, Widdicks, Duck, and Newton, 2003. Universal option valuation using quadrature methods. Journal of Financial Economics 67, 447–471 (see also Corrigendum, Journal of Financial Economics 73, 603 (2004)) is significantly extended to cover notably more complex and difficult problems in option valuations involving one or more underlyings. Trials comparing several techniques in the literature, adapted from standard lattice, grid and Monte Carlo methods to tackle particular types of problem, show that QUAD offers far greater flexibility, superior convergence, and hence, increased accuracy and considerably reduced computational times. The speed advantage of QUAD means that, even under the curse of dimensionality, it is not necessary to resort to Monte Carlo methods (certainly for options involving up to five underlying assets). Given the universality and flexibility of the method, it should be the method of choice for pricing options involving multiple underlying assets, in the presence of many features, such as early exercise or path dependency.

This paper proposes and develops a novel, simple, widely applicable numerical approach for option pricing based on quadrature methods. Though in some ways similar to lattice or finite-difference schemes, it possesses exceptional accuracy and speed. Discretely monitored options are valued with only one timestep between observations, and nodes can be perfectly placed in relation to discontinuities. Convergence is improved greatly; in the extrapolated scheme, a doubling of points can reduce error by a factor of 256. Complex problems (e.g., fixed-strike lookback discrete barrier options) can be evaluated accurately and orders of magnitude faster than by existing methods.