No-arbitrage bounds for the forward smile given marginals

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Title: No-arbitrage bounds for the forward smile given marginals
Authors: Badikov, SB
Jacquier, A
Liu, DQ
Roome, PR
Item Type: Journal Article
Abstract: We explore the robust replication of forward-start straddles given quoted (Call and Put options) market data. One approach to this problem classically follows semi-infinite linear programming arguments, and we propose a discretisation scheme to reduce its dimensionality and hence its complexity. Alternatively, one can consider the dual problem, consisting in finding optimal martingale measures under which the upper and the lower bounds are attained. Semi-analytical solutions to this dual problem were proposed by Hobson and Klimmek and by Hobson and Neuberger. We recast this dual approach as a finite dimensional linear programme, and reconcile numerically, in the Black-Scholes and in the Heston model, the two approaches.
Issue Date: 1-Feb-2017
Date of Acceptance: 25-Nov-2016
URI: http://hdl.handle.net/10044/1/42941
DOI: https://dx.doi.org/10.1080/14697688.2016.1267392
ISSN: 1469-7696
Publisher: Taylor & Francis
Start Page: 1243
End Page: 1256
Journal / Book Title: Quantitative Finance
Volume: 17
Issue: 8
Copyright Statement: © 2017 Informa UK Limited, trading as Taylor & Francis Group. This is an Accepted Manuscript of an article published by Taylor & Francis in Quantitative Finance on Feb 2017, available online: http://www.tandfonline.com/doi/full/10.1080/14697688.2016.1267392
Sponsor/Funder: Engineering & Physical Science Research Council (EPSRC)
Funder's Grant Number: EP/M008436/1
Keywords: Martingale optimal transport
Robust bounds
Forward-start
Heston
Finance
01 Mathematical Sciences
15 Commerce, Management, Tourism And Services
14 Economics
Publication Status: Published
Appears in Collections:Financial Mathematics
Mathematics
Faculty of Natural Sciences



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