Using the Malliavin calculus in time inhomogeneous jump-diffusion models, we obtain an expression for the sensitivity Theta of an option price (with respect to maturity) as the expectation of the option payoff multiplied by a stochastic weight. This expression is used to design efficient numerical algorithms that are compared with traditional finite-difference methods for the computation of Theta. Our proof can be viewed as a generalization of Dupire's integration by parts to arbitrary and possibly non-smooth payoff functions. In the time homogeneous case, Theta admits an expression from the Black-Scholes PDE in terms of Delta and Gamma but the representation formula obtained in this way is different from ours. Numerical simulations are presented in order to compare the efficiency of the finite-difference and Malliavin methods.Applied mathematical finance, European financial markets, Computational finance, Financial mathematics,
Social capital theory generally analyses network structures by focusing on the connections between players. However, it has been suggested by several authors that the absence of relations in a network or ‘structural holes’ is meaningful. The aim of our paper is to provide a global survey and appraisal of the academic research on structural holes and discuss its main measurements. We adopt a bibliometric approach and identify a typology of practices, developments, and issues related to structural holes. We highlight a strand of work on operationalization of structural holes, and discuss the various measures they propose. We provide numerical examples emphasizing the respective advantages and limitations of the studied measures. Based on our results, we propose a guide to using existing measures of structural holes according to the type (simple or complex) of network.
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