Robust hedging of the lookback option

Martingale Optimal Transport and Robust Hedging in Continuous Time

“…Hence, the portfolio of an investor consists of static positions in the call options in addition to the usual dynamically updated risky asset. This leads us to a similar structure to that in [19] and in other papers [6,8,10,11,14,15,18,21,22,23,24,25,29] which consider modelindependent pricing. This approach is very closely related to path-wise proofs of well-known probabilistic inequalities [2,9].…”

Perfect option hedging for a large trader

“…This result has independently been proven by Bergman, Grundy, and Wiener (1995) and, using a probabilistic argument, by El Karoui, Jeanblanc-Picqu e, and Shreve (1995) and Hobson (1996). It is now easy to proof Theorem 4.2 using Propositions 4.3 and 4.4 see Appendix A.2.…”

Model uncertainty and the pricing of American options

“…It might be expected that very little can be said with this approach, but the model-free literature ( [18,6,20,8,13,19,22,21,23,3,15,1]) shows that if we take the prices of vanilla options as given, and only consider martingale models which are consistent with these prices, then we can find non-trivial bounds on the prices of exotic derivatives. In this literature the idea is to not specify a model, or even a probability space or filtration.…”

“…Originating with work of Hobson [18] for lookback options, model-free or robust bounds have been identified for barrier options (Brown, Hobson, and Rogers [6]), double no touch options (Cox and Obloj [13]), basket options (Hobson, Laurence and Wang [20]), variance swaps (Hobson and Klimmek [21]), options on variance (Carr and Lee [8]) and forward start options (Hobson and Neuberger [22]). Kahalé [23] describes a general approach via convex programming for pricing and hedging European path-dependent claims in the presence of European options, using a set-up which is similar to that in the main part of this paper.…”