1 research outputs found
No-arbitrage bounds for the forward smile given marginals
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.Comment: 20 pages, 20 figure