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Department of Mathematics, Applied Mathematics and Statistics

Department of Mathematics, Applied Mathematics and Statistics

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Home / Abstracts / Ph.D. Defense- March 28, 2014

Ph.D. Defense- March 28, 2014

Posted on March 25, 2014

Friday, March 28, 2014 (2:30 p.m. in Yost 306)

Title: Multi-Scale Modeling and Analysis of Options Markets

Speaker: Charles Joseph (Case Western Reserve University)

Abstract: The fundamental question addressed in this thesis is: How
does the mood of the traders affect a derivative markets? In lack of a
reliable ground truth, a modeling-based approach is taken. First, we
develop an agent based model that simulates the behavior of traders,
characterized by few parameters that we associate to the mood. The
effects related to different distributions of investors are observed
via the time series of implied volatility surfaces of an option. To
extract information out of the volatility surfaces, it has been found
to be useful to reduce the dimensionality of the data. Typical model
reduction involves low-rank approximation techniques, such as
Principal Component analysis (PCA) or Nonnegative Matrix Factorization
(NMF) algorithms. Principal component analysis and nonnegative matrix
factorization have been successful in identifying market
characteristics of different moods.