Herd behavior index for bespoke baskets: approximation via convex ordering

Li, Churui

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https://hdl.handle.net/2142/110598 Copy

Description

Title

Herd behavior index for bespoke baskets: approximation via convex ordering

Author(s)

Li, Churui

Issue Date

2021-04-30

Director of Research (if dissertation) or Advisor (if thesis)

• Linders, Daniël
• Chong, Alfred

Department of Study

Mathematics

Discipline

Actuarial Science

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

M.S.

Degree Level

Thesis

Keyword(s)

implied dependence, comonotonicity, multivariate modeling, calibration

Abstract

In this thesis we investigate the problem of measuring dependence between stock prices only based on today's vanilla options by applying the Herd Behavior Index in bespoke baskets. The HIX is a measure of implied degree of co-movement of stocks over a given time and could be used to indicate the level of positive dependence between stocks. The calculation of the HIX requires the market data of option on each component stock and option on the basket. However, for bespoke baskets, there are only vanilla options but not basket options traded in the market. Hence, in order to calculate its HIX, we need an approach for efficient basket option pricing. In the multivariate Variance Gamma model framework, we price the bespoke basket option via convex order and comonotonic approximations which serve the purpose. We then calibrate two customized baskets using market data from 2007 to 2011. The resulting HIX indicates potential hedging possibility even during the financial crisis when most stocks are expected to move down at the same time.

Graduation Semester

2021-05

Type of Resource

Thesis

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http://hdl.handle.net/2142/110598

Copyright and License Information

Copyright 2021 Churui Li

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