No-Arbitrage Bounds for the Forward Smile Given Marginals

20 Pages Posted: 28 Mar 2016 Last revised: 7 Oct 2016

See all articles by Sergey Badikov

Sergey Badikov

Imperial College London

Antoine (Jack) Jacquier

Imperial College London; The Alan Turing Institute

Qing Liu

Imperial College London-Department of Mathematics

Patrick Roome

Imperial College London - Department of Mathematics

Date Written: March 21, 2016

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.

Keywords: Optimal transport, forward smile, linear programme

Suggested Citation

Badikov, Sergey and Jacquier, Antoine and Liu, Qing and Roome, Patrick, No-Arbitrage Bounds for the Forward Smile Given Marginals (March 21, 2016). Available at SSRN: https://ssrn.com/abstract=2755274 or http://dx.doi.org/10.2139/ssrn.2755274

Sergey Badikov

Imperial College London ( email )

South Kensington Campus
Exhibition Road
London, Greater London SW7 2AZ
United Kingdom

Antoine Jacquier

Imperial College London ( email )

South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom

HOME PAGE: http://wwwf.imperial.ac.uk/~ajacquie/

The Alan Turing Institute ( email )

British Library, 96 Euston Road
London, NW12DB
United Kingdom

Qing Liu

Imperial College London-Department of Mathematics ( email )

South Kensington Campus,Imperial College
LONDON, SW7 2AZ
United Kingdom

Patrick Roome (Contact Author)

Imperial College London - Department of Mathematics ( email )

South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom

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