The scaling limit of superreplication prices with small transaction costs in the multivariate case

Peter Bank; Yan Dolinsky; Ari Pekka Perkkiö

doi:10.1007/s00780-016-0320-4

The scaling limit of superreplication prices with small transaction costs in the multivariate case

Peter Bank^*, Yan Dolinsky, Ari Pekka Perkkiö

^*Corresponding author for this work

Department of Statistics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

Kusuoka (Ann. Appl. Probab. 5:198–221, 1995) showed how to obtain non-trivial scaling limits of superreplication prices in discrete-time models of a single risky asset which is traded at properly scaled proportional transaction costs. This article extends the result to a multivariate setup where the investor can trade in several risky assets. The G-expectation describing the limiting price involves models with a volatility range around the frictionless scaling limit that depends not only on the transaction costs coefficients, but also on the chosen complete discrete-time reference model.

Original language	American English
Pages (from-to)	487-508
Number of pages	22
Journal	Finance and Stochastics
Volume	21
Issue number	2
DOIs	https://doi.org/10.1007/s00780-016-0320-4
State	Published - 1 Apr 2017

Bibliographical note

Funding Information:
The authors are grateful to the Einstein Foundation for the financial support through its research project on “Game options and markets with frictions”.

Publisher Copyright:
© 2016, Springer-Verlag Berlin Heidelberg.

Keywords

Complete model
Limit theorems
Superreplication
Transaction costs

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10.1007/s00780-016-0320-4

Cite this

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AB - Kusuoka (Ann. Appl. Probab. 5:198–221, 1995) showed how to obtain non-trivial scaling limits of superreplication prices in discrete-time models of a single risky asset which is traded at properly scaled proportional transaction costs. This article extends the result to a multivariate setup where the investor can trade in several risky assets. The G-expectation describing the limiting price involves models with a volatility range around the frictionless scaling limit that depends not only on the transaction costs coefficients, but also on the chosen complete discrete-time reference model.

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The scaling limit of superreplication prices with small transaction costs in the multivariate case

Abstract

Bibliographical note

Keywords

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