Perturbation Analysis of Sub/Super Hedging Problems

29 Pages Posted: 28 Jun 2018

See all articles by Sergey Badikov

Sergey Badikov

Imperial College London

Mark Davis

Imperial College London

Antoine (Jack) Jacquier

Imperial College London; The Alan Turing Institute

Date Written: June 12, 2018

Abstract

We investigate the links between various no-arbitrage conditions and the existence of pricing functionals in general markets, and prove the Fundamental Theorem of Asset Pricing therein. No-arbitrage conditions, either in this abstract setting or in the case of a market consisting of European Call options, give rise to duality properties of infinite-dimensional sub- and super-hedging problems. With a view towards applications, we show how duality is preserved when reducing these problems over finite-dimensional bases. We finally perform a rigorous perturbation analysis of those linear programming problems, and highlight, as a numerical example, the influence of smile extrapolation on the bounds of exotic options.

Keywords: duality, infinity-dimensional linear programming, super-hedging, perturbation methods

JEL Classification: 90C05, 90C46, 91G20, 46N10

Suggested Citation

Badikov, Sergey and Davis, Mark and Jacquier, Antoine, Perturbation Analysis of Sub/Super Hedging Problems (June 12, 2018). Available at SSRN: https://ssrn.com/abstract=3194935 or http://dx.doi.org/10.2139/ssrn.3194935

Sergey Badikov

Imperial College London ( email )

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

Mark Davis

Imperial College London ( email )

South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom
02075948486 (Phone)

HOME PAGE: http://www.ma.ic.ac.uk/~mdavis

Antoine Jacquier (Contact Author)

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

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