CFRM 405: Mathematical Methods for Quantitative Finance Homework 1
Instructions: Solve each of the exercises both by hand (must show all work for credit).
1. Compute the following limits.
2. Compute the derivatives of the following functions.
(the {ak} are constants)
(K > 0, r, q, σ > 0, and T > t constant)
(S > 0, K > 0, r, q, and T > t constant)
0, and T > t constant) 3. Recall that
(a) Parts (c), (d), and (e) of Problem 2 correspond to partial derivatives of d+. What partial derivative does each correspond to?
(b) Compute the partial derivative of d+ with respect to t.
4. Compute the following antiderivatives.
Z
(a) x2 log(x)dx
Z
(b) x2exdx
