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On gamma estimation via matrix kriging
Author(s) -
Yun Xin,
Hong L. Jeff,
Jiang Guangxin,
Wang Shouyang
Publication year - 2019
Publication title -
naval research logistics (nrl)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 68
eISSN - 1520-6750
pISSN - 0894-069X
DOI - 10.1002/nav.21850
Subject(s) - cholesky decomposition , greeks , mathematical optimization , computer science , risk management , constraint (computer aided design) , matrix (chemical analysis) , derivative (finance) , element (criminal law) , mathematics , finance , eigenvalues and eigenvectors , economics , physics , geometry , materials science , quantum mechanics , political science , financial economics , law , composite material
In financial engineering, sensitivities of derivative prices (also known as the Greeks) are important quantities in risk management, and stochastic gradient estimation methods are used to estimate them given the market parameters. In practice, the surface (function) of the Greeks with respect to the underlying parameters is much more desired, because it can be used in real‐time risk management. In this paper, we consider derivatives with multiple underlying assets, and propose three stochastic kriging‐based methods, the element‐by‐element, the importance mapping, and the Cholesky decomposition, to fit the surface of the gamma matrix that can fulfill the time constraint and the precision requirement in real‐time risk management. Numerical experiments are provided to illustrate the effectiveness of the proposed methods.