Geometric extension of put-call symmetry in the multiasset setting
In this paper we show how to relate European call and put options on multiple assets to certain convex bodies called lift zonoids. Based on this, geometric properties can be translated into economic statements and vice versa. For instance, the European call-put parity corresponds to the central symmetry property, while the concept of dual markets can be explained by reflection with respect to a plane. It is known that the classical univariate log-normal model belongs to a large class of distributions with an extra property, analytically known as put-call symmetry. The geometric interpretation of this symmetry property motivates a natural multivariate extension. The financial meaning of this extension is explained, the asset price distributions that have this property are characterised and their further properties explored. It is also shown how to relate some multivariate asymmetric distributions to symmetric ones by a power transformation that is useful to adjust for carrying costs. A particular attention is devoted to the case of asset prices driven by L\'evy processes. Based on this, semi-static hedging techniques for multiasset barrier options are suggested.
Year of publication: |
2008-06
|
---|---|
Authors: | Molchanov, Ilya ; Schmutz, Michael |
Institutions: | arXiv.org |
Saved in:
freely available
Saved in favorites
Similar items by person
-
Exchangeability type properties of asset prices
Molchanov, Ilya, (2009)
-
Intragroup transfers, intragroup diversification and their risk assessment
Haier, Andreas, (2016)
-
Static replications with traffic light options
Schmutz, Michael, (2010)
- More ...