No-arbitrage bounds for the forward smile given marginals

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

Quantitative Finance, 2017, vol. 17, issue 8, 1243-1256

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 [Financ. Stochastics, 2015, 19, 189–214] and by Hobson and Neuberger [Math. Financ., 2012, 22, 31–56]. We recast this dual approach as a finite-dimensional linear program, and reconcile numerically, in the Black–Scholes and in the Heston model, the two approaches.

Date: 2017
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DOI: 10.1080/14697688.2016.1267392

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