Algorithm 1 Estimation of state price density of a basket

Input: Basket option prices,

Output: and, , that minimize the squared loss

Method:

1. Choose by cross-validation

2. Initialize and evenly in

3. While not converge do

4. Update ‘s by Newton Ralphson iteration given current ‘s

5. Update ‘s by quadratic solvers given current ‘s

6. end while

7. Return and,