Browsing by Author "Liu, Xiao"
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Item Accounting Standards, Capital Regulation and Credit Supply: A Reduced-form and Structural Analysis(2023-04-21) Liu, Xiao; Sivaramakrishnan, ShivaPrior research has examined how accounting rules and capital regulation each impact bank lending, but few studies have investigated their combined effects. In this dissertation, I propose and test the thesis that bank capitalization and loan-loss reserving jointly affect credit supply during economic downturns. Specifically, I use the Global Financial Crisis as a context to analyze the usability of capital buffers in conjunction with the adequacy of loan-loss reserving. Contrary to conventional wisdom that capital buffers mitigate procyclicality in lending, my analysis reveals that both high and low regulatory capital buffer banks reduced lending during the crisis. More importantly, crisis-lending is inversely related to the size of the buffer for high regulatory buffer banks. This result suggests that these banks likely had higher risk exposures in their loan portfolios prior to the crisis and faced the prospect of greater unexpected losses. Moreover, I show that adequate loan-loss reserving under the prevailing accounting rules (the Incurred Loss method or ICL) reduces pro-cyclicality for both low and high regulatory capital buffer banks. Furthermore, I investigate the efficacy of the new Current Expected Credit Loss (CECL) model. The CECL model was implemented with the intent of inducing banks to set aside sufficient loan-loss reserves. By calibrating a loan portfolio migration model, I find that under CECL, banks hold less capital, earn lower profits, and lend less during both expansion and contraction periods. Additionally, provisions surge more dramatically under CECL following an unanticipated contraction, hindering lending and profitability. These results suggest that lending is more pro-cyclical under CECL than ICL, despite its intended purpose to maintain credit supply and reduce procyclicality.Item Structured matrix algorithms for solving Helmholtz equation(2019-04-12) Liu, Xiao; de Hoop, Maarten VIn this dissertation, novel solution algorithms are developed for large structured linear systems such as the discretized Helmholtz equation. Firstly, we develop two parallel randomized algorithms for constructing hierarchically semiseparable (HSS) matrices. Randomized sampling reduces the computational complexity and the communication cost simultaneously, and the resulting method is suitable for solving dense systems arising from multiple scattering problems. Secondly, a direct factorization update algorithm is proposed for solving the Helmholtz equation with changing wavespeed. The data dependency among a set of interior and exterior sub-problems is exploited to maximize the data reuse and to minimize the propagation of changes. Thirdly, interconnected HSS structures are designed to improve the efficiency of rank-structured factorization of PDE problems. Intermediate Schur complements at different levels share the same set of HSS bases during the factorization. Finally, we propose a contour integration preconditioner for solving 3D high-frequency Helmholtz equation. By solving systems with complex shifts, the problem is projected in subspaces with faster GMRES convergence. The shifted problems are solved by a polynomial fixed-point iteration, which is robust when the shift changes.