MAFS 5030
Quantitative Modeling of Derivatives Securities
Solution to Homework Two
Course Instructor: Prof. Y.K. Kwok
1. part: The trading strategy H with V0 < 0 and V1 ( ) 0, , dominates the zero-holding trading strategy H = (0 0 0)T . The zeroholding st
MAFS 5030
Quantitative Modeling of Derivatives Securities
Solution to Homework Three
Course Instructor: Prof. Y.K. Kwok
1. F is generated by the partition P = cfw_3, 2, cfw_1, 1, cfw_2, 3.
(i) Since cfw_2, 3 P and X (2) = 4 = X (3) = 9, X is not F -measur
MAFS 5030
Quantitative Modeling of Derivatives Securities
Solution to Homework One
Course Instructor: Prof. Y.K. Kwok
1. There will be two coupons before delivery: one in 6 months and one just prior to
delivery. Using the present value formula:
$94.6 =
F
MAFS 5030 - Quantitative Modeling of Derivatives Securities
Solution to Homework Four
1. (a) It is easily seen that
t+s
k2
X1 (t + s) X1 (s) = k Z
s
k2
Z
+
is normally distributed with mean zero and variance k 2 tk2s ks2 = t. Also
the increments X1 (ti+1
MAFS 5030
Quantitative Modeling of Derivatives Securities
Homework Two
Course Instructor: Prof. Y.K. Kwok
1. Show that a dominant trading strategy exists if and only if there exists a trading strategy satisfying V0 < 0
and V1 () 0 for all .
Hint: Consider
MAFS 5030
Quantitative Modeling of Derivatives Securities
Homework One
Course Instructor: Prof. Y.K. Kwok
1. Consider a one-year forward contract whose underlying asset is a coupon paying bond with maturity
date beyond the expiration date of the forward c
MAFS 5030
Quantitative Modeling of Derivatives Securities
Homework Four
Course Instructor: Prof. Y.K. Kwok
1. Consider the Brownian motion with drift dened by
X (t) = t + Z (t),
X (0) = 0, Z (t) is the standard Brownian motion,
nd E [X (t)|X (t0)], var(X
MAFS 5030
Quantitative Modeling of Derivatives Securities
Homework Five
Course Instructor: Prof. Y.K. Kwok
1. Consider a European capped call option whose terminal payo function is given by
cM (S, 0; X, M ) = min(max(S X, 0), M ),
where X is the strike pr