15,507 research outputs found
Exchangeability type properties of asset prices
In this paper we analyse financial implications of exchangeability and
similar properties of finite dimensional random vectors. We show how these
properties are reflected in prices of some basket options in view of the
well-known put-call symmetry property and the duality principle in option
pricing. A particular attention is devoted to the case of asset prices driven
by Levy processes. Based on this, concrete semi-static hedging techniques for
multi-asset barrier options, such as certain weighted barrier spread options,
weighted barrier swap options or weighted barrier quanto-swap options are
suggested.Comment: The final version of the paper "Semi-static hedging under
exchangeability type conditions". To appear in Advances in Applied
Probabilit
Data depth and floating body
Little known relations of the renown concept of the halfspace depth for
multivariate data with notions from convex and affine geometry are discussed.
Halfspace depth may be regarded as a measure of symmetry for random vectors. As
such, the depth stands as a generalization of a measure of symmetry for convex
sets, well studied in geometry. Under a mild assumption, the upper level sets
of the halfspace depth coincide with the convex floating bodies used in the
definition of the affine surface area for convex bodies in Euclidean spaces.
These connections enable us to partially resolve some persistent open problems
regarding theoretical properties of the depth
Semi-Static Hedging Based on a Generalized Reflection Principle on a Multi Dimensional Brownian Motion
On a multi-assets Black-Scholes economy, we introduce a class of barrier
options. In this model we apply a generalized reflection principle in a context
of the finite reflection group acting on a Euclidean space to give a valuation
formula and the semi-static hedge.Comment: Asia-Pacific Financial Markets, online firs
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