Index options and model-free measurement of herd behavior in stock markets

In the first chapter of this course, we investigate model-free upper bounds for index option prices. These bounds are based on convex upper bounds for sums of r.v.’s, see Dhaene, Denuit, Goovaerts, Kaas & Vyncke (2002) and on the decomposition formula for stop-loss premiums of a sum of comonotonic r.v.’s, presented in Dhaene, Wang, Young & Goovaerts (1998) and in Kaas, Dhaene & Goovaerts (2000). These bounds for index option prices can be expressed in terms of the prices of options on the different stocks of which the index is composed, see Chen, Deelstra, Dhaene & Vanmaele (2008) and Linders, Dhaene, Hounnon and Vanmaele (2012).  

In the second chapter, we use observed index option prices and their comonotonic upper bounds (derived in chapter 1) to define the Herd Behavior Index (HIX), which is a model-free measure for the implied degree of co-movement between the stocks, see Dhaene, Linders, Schoutens & Vynke (2012) and Linders, Dhaene & Schoutens (2015). We explain in detail how the HIX can be calculated in real time, simply based on observed index option prices and option prices on the components of which the index is composed. 

* All references mentioned above can be downloaded from

Chapter 1: Model-free upper bounds for index option prices.  
– Presentation: [pdf]
– Main references:
Chen X., Deelstra G., Dhaene J. & Vanmaele M. (2008). Static super-replicating strategies for a class of exotic options. Insurance: Mathematics and Economics 42(3), 1067-1085. [pdf]
Linders D., Dhaene J., Hounnon H. & Vanmaele M. (2012). Index options: a model-free approach. Research Report AFI-1265, FEB, KU Leuven. [pdf]

Chapter 2: Implied co-movement behavior in stock markets.
– Presentation: [pdf]
– Main references:
Dhaene J., Linders D., Schoutens W. & Vyncke D. (2012). The Herd Behavior Index: a new  measure for the implied degree of co-movement in financial markets. Insurance: Mathematics and Economics 50(3), 357-370. [pdf]
Linders D., Dhaene J., Schoutens W. (2015). Option prices and model-free measurement of implied herd behavior in stock markets. International Journal of Financial Engineering 2(2), 15550012. [pdf]