### 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.