This paper presents a method for computing upper and lower bounds on the price of a European basket call option, given prices on other similar options. The authors show that in some cases, these bounds can be computed using simple closed-form expressions or linear programs. They also introduce an efficient linear programming relaxation of the general problem based on an integral transform interpretation of the call price function. This relaxation is shown to be tight in some special cases. The paper begins by introducing the problem of computing bounds on the price of a European basket call option, given prices on other similar options. The authors then discuss the use of linear programming and duality theory to derive these bounds. They show that the problem can be formulated as a semi-infinite linear program, and that this can be relaxed to a finite linear program. The authors then present results on the tightness of the linear programming relaxation in the general case. They show that the relaxation is tight in some special cases, and that it can be used to compute exact bounds in other cases. They also show that the relaxation is tight when only single asset option prices are given for many strikes. The paper concludes with numerical results showing how the method can be used to clean market data on single asset option prices and to compute bounds on the price of a basket given other basket prices. The authors also show that the relaxation is not tight in the lower bound case, and that the lower bound computed in section 3.3 is larger than the relaxation’s result in some cases.This paper presents a method for computing upper and lower bounds on the price of a European basket call option, given prices on other similar options. The authors show that in some cases, these bounds can be computed using simple closed-form expressions or linear programs. They also introduce an efficient linear programming relaxation of the general problem based on an integral transform interpretation of the call price function. This relaxation is shown to be tight in some special cases. The paper begins by introducing the problem of computing bounds on the price of a European basket call option, given prices on other similar options. The authors then discuss the use of linear programming and duality theory to derive these bounds. They show that the problem can be formulated as a semi-infinite linear program, and that this can be relaxed to a finite linear program. The authors then present results on the tightness of the linear programming relaxation in the general case. They show that the relaxation is tight in some special cases, and that it can be used to compute exact bounds in other cases. They also show that the relaxation is tight when only single asset option prices are given for many strikes. The paper concludes with numerical results showing how the method can be used to clean market data on single asset option prices and to compute bounds on the price of a basket given other basket prices. The authors also show that the relaxation is not tight in the lower bound case, and that the lower bound computed in section 3.3 is larger than the relaxation’s result in some cases.