Static-arbitrage optimal subreplicating strategies for basket options

Hobson, David; Laurence, Peter; Wang, Tai‐Ho

doi:10.1016/j.insmatheco.2005.05.010

Cited by 50 publications

(50 citation statements)

References 13 publications

(14 reference statements)

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“…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].…”

Section: Introductionsupporting

confidence: 64%

Martingale Optimal Transport and Robust Hedging in Continuous Time

Dolinsky

Soner

2013

SSRN Journal

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Abstract. The duality between the robust (or equivalently, model independent) hedging of path dependent European options and a martingale optimal transport problem is proved. The financial market is modeled through a risky asset whose price is only assumed to be a continuous function of time. The hedging problem is to construct a minimal super-hedging portfolio that consists of dynamically trading the underlying risky asset and a static position of vanilla options which can be exercised at the given, fixed maturity. The dual is a Monge-Kantorovich type martingale transport problem of maximizing the expected value of the option over all martingale measures that have a given marginal at maturity. In addition to duality, a family of simple, piecewise constant super-replication portfolios that asymptotically achieve the minimal super-replication cost is constructed.

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Section: Introductionsupporting

confidence: 64%

Martingale Optimal Transport and Robust Hedging in Continuous Time

Dolinsky

Soner

2013

SSRN Journal

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“…The structure studied in this paper is similar to that of [19] and also of [6,9,10,11,13,14,15,18,21,22,23,24,25,27]. We refer the reader to the excellent survey of Hobson [20] and to our previous papers [15,16] and to the references therein.…”

Section: 3) |G(s)| ≤ C(1 + |S T |)mentioning

confidence: 74%

Martingale optimal transport in the Skorokhod space

Dolinsky

Soner

2015

Stochastic Processes and their Applications

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Abstract. The dual representation of the martingale optimal transport problem in the Skorokhod space of multi dimensional cádlág processes is proved. The dual is a minimisation problem with constraints involving stochastic integrals and is similar to the Kantorovich dual of the standard optimal transport problem. The constraints are required to hold for very path in the Skorokhod space. This problem has the financial interpretation as the robust hedging of path dependent European options.

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“…The classical Fréchet-Hoeffding bounds therefore lead to model-free price estimates for such options [1], [4], [5], [12].…”

Section: A (Two-dimensional) Copula Is a Functionmentioning

confidence: 99%

Improved Fréchet Bounds and Model-Free Pricing of Multi-Asset Options

Tankov

2011

J. Appl. Probab.

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Improved bounds on the copula of a bivariate random vector are computed when partial information is available, such as the values of the copula on a given subset of [0, 1] 2 , or the value of a functional of the copula, monotone with respect to the concordance order. These results are then used to compute model-free bounds on the prices of two-asset options which make use of extra information about the dependence structure, such as the price of another two-asset option.

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Static-arbitrage optimal subreplicating strategies for basket options

Cited by 50 publications

References 13 publications

Martingale Optimal Transport and Robust Hedging in Continuous Time

Martingale Optimal Transport and Robust Hedging in Continuous Time

Martingale optimal transport in the Skorokhod space

Improved Fréchet Bounds and Model-Free Pricing of Multi-Asset Options

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