Template-Type: ReDIF-Paper 1.0
Title: Hedging Basket Options by Using a Subset of
	Underlying Assets
Author-Name: Xia Su
Author-Email: xia.su@uni-bonn.de
Classification-JEL: G13
Keywords: Basket options, Principal Components Analysis, Super-replication, Expected
	shortfall
Abstract: This paper proposes two-step static hedging strategies for
	European basket options by using only plain-vanilla
	options on a subset of underlying assets. The basic idea
	is stimulated from a static super-hedging strategy
	dependent on the whole basket. However, it would be too
	complicated to handle when there is a large number of
	assets in the basket. It becomes even worse when some of
	the underlying assets are illiquid or not available for
	trading. Meanwhile, this strategy completely neglects the
	correlation structure of the basket which has indeed a
	great effect on the basket option's price. To solve these
	problems, Principal Components Analysis is used to figure
	out the subset of
	dominant assets through a careful study on the modified
	covariance of the basket. On this basis, the optimal
	strikes of those significant assets' plain-vanilla options
	are obtained in the second step via optimization. The
	optimality criterion depends on the risk attitude of
	hedgers and is defined by a certain risk measure, e.g.,
	super-replication, minimum expected shortfall given a
	constraint on the hedging cost. Through analyzing a
	numerical example, it is concluded that this static
	hedging portfolio captures a trade-off between reduced
	hedging costs and overall super-replication. Even without
	considering transaction costs, hedging by using only a
	subset of underlying assets performs well: only a
	reasonable small hedging error arises when investing the
	capital required by the super-hedging portfolio which is
	composed of plain-vanilla options on all underlying assets
	and hence is difficult to implement or even not available
	in the market.
Note: 
Length: 32
Creation-Date: 2006-06	
Revision-Date: 
File-URL: http://www.wiwi.uni-bonn.de/bgsepapers/bonedp/bgse14_2006.pdf
File-Format: application/pdf
Handle: RePEc:bon:bonedp:bgse14_2006