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

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 boun...

• Type: Journal
• Year: 2010
• Where: AOR
• Authors: Javier Peña, Xavier Saynac, Juan Carlos Vera, Luis Fernando Zuluaga
• Keywords: AOR 2010, Arbitrage, Artificial Intelligence, European Basket Options, Lower Arbitrage