Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  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,  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 lor 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 lor 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.  illustrate our results by computing upper and lor arbitrage bounds on gasoline/heating oil crack spread options.
['Javier Peña', 'Xavier Saynac', 'Juan Carlos Vera', 'Luis F. Zuluaga']
I am writing a research paper on a idea Computing general static-arbitrage bounds for European basket options via Dantzig-Wolfe decomposition
[{"from": "human", "value": "I am writing a research paper on a idea Computing general static-arbitrage bounds for European basket options via Dantzig-Wolfe decomposition"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  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,  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 lor 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 lor 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.  illustrate our results by computing upper and lor arbitrage bounds on gasoline/heating oil crack spread options."}]