Model-independent bounds for option prices—a mass transport approach

By Mathias Beiglbock, Pierre Henry-Labordère, Friedrich Penkner. Finance and Stochastics, 2011

402 citations recorded by the source corpus.

In this paper we investigate model-independent bounds for exotic options written on a risky asset using infinite-dimensional linear programming methods. Based on arguments from the theory of Monge–Kantorovich mass transport, we establish a dual version of the problem that has a natural financial interpretation in terms of semi-static hedging. In particular we prove that there is no duality gap.

Subfields: Finance, Global and Planetary Change

View Paper: https://www.semanticscholar.org/paper/ce18245fe4f78e0c6221d3a10139eaf77eddb76a

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Citations in the corpus

The maximum maximum of a martingale with given $\mathbf{n}$ marginals (2012, background): “The ﬁrst one, reported in Section 4, consists in a short pathwise argument, based on a guess of the form of the optimal superhedging strategy for a simple one-touch barrier option, combined with the Skorokhod embedding results of [33].”
UTILITY MAXIMIZATION UNDER MODEL UNCERTAINTY IN DISCRETE TIME (2013, background): “The robust superhedging problem has been studied in several settings; see [1, 4, 6, 11, 13, 17, 23, 26, 32, 33], among others.”
Multi-marginal optimal transport: theory and applications (2014, background): “This has quickly become a very active area; see for example [3, 4, 25, 26, 33, 42, 43].”
On a problem of optimal transport under marginal martingale constraints (2012, background): “Therefore, any x ∈ ]0,1/5[ gives rise to the maximum of F(·, y) for three different y ∈ [−1,0]∪ [1,2].”
A MODEL‐FREE VERSION OF THE FUNDAMENTAL THEOREM OF ASSET PRICING AND THE SUPER‐REPLICATION THEOREM (2013, methodology): “By Theorem 1 in [BHLP11] we have: Corollary 4.”
Sampling of probability measures in the convex order and approximation of Martingale Optimal Transport problems (2017, neutral): “We consider μ(dx) = 121[−1,1]dx and ν(dx) = ( 1 121[−3,−1](x) + 1 31[−1,1](x) + 1 121[1,3](x) ) dx.”
Arbitrage and duality in nondominated discrete-time models (2013, methodology): “Following work of Beiglböck, Henry-Labordère and Penkner [3] in discrete time and Galichon, Henry-Labordère and Touzi [31] in continuous time, this can be used to prove the absence of a duality gap under certain regularity conditions, and in specific cases, to characterize a dual optimizer and a sup”
Multi-marginal optimal transport and multi-agent matching problems: uniqueness and structure of solutions (2012, background): “book of Villani [32]. Recently, optimal transport problems with several marginals have begun to attract more attention, due to emerging applications in economics [9] [11], mathematical ﬁnance [15][19][2], condensed matter physics [12] [6], barycenters and image processing [1] [3] and the characteriz”
Model-free superhedging duality (2015, neutral): “The reformulation of the superhedging duality in the framework of optimal mass transport led to important results both in discrete and continuous time as in [3, 11, 12, 14, 15, 20, 23].”
Martingale Benamou–Brenier: A probabilistic perspective (2017, background): “Early papers to investigate such problems include [33, 11, 53, 23, 22, 20], and this topic is commonly referred to as martingale optimal transport.”
Monotone martingale transport plans and Skorokhod embedding (2017, positive): “The martingale optimal transport problem, as introduced in [4] in the present discrete-time case and [13], is defined by:”
Decentralize and Randomize: Faster Algorithm for Wasserstein Barycenters (2018, background): “and finance [5], condensed matter physics [8], and other applications [26].”
An Explicit Martingale Version of the One-Dimensional Brenier's Theorem with Full Marginals Constraint (2016, neutral): “Recently, a martingale transportation (MT) problem was introduced in Beiglböck, Henry- Labordère & Penkner [5] and in Galichon, Henry-Labordère & Touzi [32].”
On the Monge–Kantorovich problem with additional linear constraints (2014, neutral): “ Z R φ(xk)dµk : Xn k=1 φk(xk)+ Xn−1 k=1 ρ(x1,...,xk)(xk+1 − xk) ≤ c ) . where (φk)n k=1 ∈ (CL(µk)) n k=1, ρ(x1,...,xk) ∈ Cb(Rn). This result was obtained by Beiglboeck, Henry-Labordere and Penkner in [4]. Also they show (Prop. 4.1 in [4]) that optimal value of the dual problem in this setting is not”
Computational Optimal Transport (2018, neutral): “[2014], Dolinsky and Soner [2014], Tan and Touzi [2013], Beiglböck et al. [2013]), which finds many applications in finance, imposes the so-called martingale constraint on the conditional mean of the coupling, when X = Y = Rd:”
All adapted topologies are equal (2019, neutral): “[34, 13, 27, 23, 17, 33, 18, 12, 14] among many others).”