Computing general static-arbitrage bounds for European basket options via Dantzig-Wolfe decomposition

J. Pena, X. Saynac, J.C. Vera, L.F. Zuluaga

Research output: Contribution to journalArticleScientificpeer-review

Abstract

We study the problem of computing general static-arbitrage bounds for European basket options; that is, computing bounds on the price of a basket option, given the only assumption of absence of arbitrage, and information about prices of other European basket options on the same underlying assets and with the same maturity. In particular, we provide a simple efficient way to compute this type of bounds by solving a large finite non-linear programming formulation of the problem. This is done via a suitable Dantzig-Wolfe decomposition that takes advantage of an integer programming formulation of the corresponding subproblems. Our computation method equally applies to both upper and lower arbitrage bounds, and provides a solution method for general instances of the problem. This constitutes a substantial contribution to the related literature, in which upper and lower bound problems need to be treated differently, and which provides efficient ways to solve particular static-arbitrage bounds for European basket options; namely, when the option prices information used to compute the bounds is limited to vanilla and/or forward options, or when the number of underlying assets is limited to two assets. Also, our computation method allows the inclusion of real-world characteristics of option prices into the arbitrage bounds problem, such as the presence of bid-ask spreads. We illustrate our results by computing upper and lower arbitrage bounds on gasoline/heating oil crack spread options.
Original languageEnglish
Pages (from-to)65-74
JournalAlgorithmic Operations Research
Volume5
Issue number2
Publication statusPublished - 2010

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Arbitrage
Basket option
Dantzig-Wolfe decomposition
Assets
Option prices
Inclusion
Maturity
Upper bound
Spread options
Heating
Integer programming
Nonlinear programming
Lower bounds
Bid/ask spread
Oil

Cite this

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abstract = "We study the problem of computing general static-arbitrage bounds for European basket options; that is, computing bounds on the price of a basket option, given the only assumption of absence of arbitrage, and information about prices of other European basket options on the same underlying assets and with the same maturity. In particular, we provide a simple efficient way to compute this type of bounds by solving a large finite non-linear programming formulation of the problem. This is done via a suitable Dantzig-Wolfe decomposition that takes advantage of an integer programming formulation of the corresponding subproblems. Our computation method equally applies to both upper and lower arbitrage bounds, and provides a solution method for general instances of the problem. This constitutes a substantial contribution to the related literature, in which upper and lower bound problems need to be treated differently, and which provides efficient ways to solve particular static-arbitrage bounds for European basket options; namely, when the option prices information used to compute the bounds is limited to vanilla and/or forward options, or when the number of underlying assets is limited to two assets. Also, our computation method allows the inclusion of real-world characteristics of option prices into the arbitrage bounds problem, such as the presence of bid-ask spreads. We illustrate our results by computing upper and lower arbitrage bounds on gasoline/heating oil crack spread options.",
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Computing general static-arbitrage bounds for European basket options via Dantzig-Wolfe decomposition. / Pena, J.; Saynac, X.; Vera, J.C.; Zuluaga, L.F.

In: Algorithmic Operations Research, Vol. 5, No. 2, 2010, p. 65-74.

Research output: Contribution to journalArticleScientificpeer-review

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