The Scaling Limit of Superreplication Prices with Small Transaction Costs in the Multivariate Case

Peter Bank; Yan Dolinsky; Ari-Pekka Perkkiö

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arXiv · 1510.04537

The Scaling Limit of Superreplication Prices with Small Transaction Costs in the Multivariate Case

Peter Bank·Yan Dolinsky·Ari-Pekka Perkkiö

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Abstract

Kusuoka [ Limit Theorem on Option Replication Cost with Transaction Costs, 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 multi-variate 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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Peter Bank, Yan Dolinsky, Ari-Pekka Perkkiö. 2015-10-15. The Scaling Limit of Superreplication Prices with Small Transaction Costs in the Multivariate Case. https://arxiv.org/abs/1510.04537

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