No-arbitrage bounds for the forward smile given marginals

DOI10.1080/14697688.2016.1267392zbMATH Open1402.91752arXiv1603.06389OpenAlexW3121987632MaRDI QIDQ4555138

Antoine Jacquier, Daphne Qing Liu, Sergey Badikov, Patrick Roome

Publication date: 19 November 2018

Published in: Quantitative Finance (Search for Journal in Brave)

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 (2013) and by Hobson and Neuberger (2008). 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.

Full work available at URL: https://arxiv.org/abs/1603.06389

zbMATH Keywords

martingale optimal transportHestonrobust boundsforward-start

Mathematics Subject Classification ID

Optimality conditions and duality in mathematical programming (90C46) Linear programming (90C05) Semi-infinite programming (90C34) Martingales with continuous parameter (60G44) Financial applications of other theories (91G80) Derivative securities (option pricing, hedging, etc.) (91G20)

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Related Items (3)

Perturbation analysis of sub/super hedging problems ⋮ Recent contributions to linear semi-infinite optimization: an update ⋮ Discretisation and duality of optimal Skorokhod embedding problems

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