This paper addresses the problem of computing upper and lower bounds on the price of a European basket call option, given prices of other similar options. The authors propose a linear programming relaxation based on an integral transform interpretation of the call price function, which is tight in certain special cases. They also provide exact solutions to the problem in specific cases and show that the relaxation is tight using results from [HLW04]. The paper includes numerical examples to demonstrate the effectiveness of the relaxation technique.This paper addresses the problem of computing upper and lower bounds on the price of a European basket call option, given prices of other similar options. The authors propose a linear programming relaxation based on an integral transform interpretation of the call price function, which is tight in certain special cases. They also provide exact solutions to the problem in specific cases and show that the relaxation is tight using results from [HLW04]. The paper includes numerical examples to demonstrate the effectiveness of the relaxation technique.