Explicit characterization of the super-replication strategy in financial markets with partial transaction costs
Bouchard, Bruno; Ben Tahar, Imen (2007), Explicit characterization of the super-replication strategy in financial markets with partial transaction costs, Stochastic Processes and their Applications, 117, 5, p. 655-672. http://dx.doi.org/10.1016/j.spa.2006.09.010
Type
Article accepté pour publication ou publiéExternal document link
http://hal.archives-ouvertes.fr/hal-00003546/en/Date
2007Journal name
Stochastic Processes and their ApplicationsVolume
117Number
5Publisher
Elsevier
Pages
655-672
Publication identifier
Metadata
Show full item recordAbstract (EN)
We consider a continuous time multivariate financial market with proportional transaction costs and study the problem of finding the minimal initial capital needed to hedge, without risk, European-type contingent claims. The model is similar to the one considered in Bouchard and Touzi [B. Bouchard, N. Touzi, Explicit solution of the multivariate super-replication problem under transaction costs, The Annals of Applied Probability 10 (3) (2000) 685–708] except that some of the assets can be exchanged freely, i.e. without paying transaction costs. In this context, we generalize the result of the above paper and prove that the super-replication price is given by the cost of the cheapest hedging strategy in which the number of non-freely exchangeable assets is kept constant over time. Our proof relies on the introduction of a new auxiliary control problem whose value function can be interpreted as the super-hedging price in a model with unbounded stochastic volatility (in the directions where transaction costs are non-zero). In particular, it confirms the usual intuition that transaction costs play a similar role to stochastic volatility.Subjects / Keywords
Mathematical Finance; Hedging options; viscosity solutions; Non efficient transaction costsJEL
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