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STAT/ACTSC 446/846
Assignment #5 (due December 4, 2009)
13.
Problems from the textbook:
Chapter 13:
13.5, 13.14, and 13.16
4. Using the riskneutral pricing formula, ﬁnd a closedform expression for the price at time
t
= 0 of
a call option with maturity
T
and strike
K
. Assume that the continuously compounded interest
rate
r
is constant and that the price of a risky asset follows a geometric Brownian motion with
volatility parameter
σ
. Show all steps in your derivation.
5. Denote the European call option price in the BlackScholes model by
C
(
S
). Find an expression
for the delta of the option
∂
∂S
C
(
S
). Show all your calculations.
6. Suppose that under the realworld measure
P
, the short interest rate
r
follows the model
dr
t
=
σdW
t
.
The initial spot rate
r
0
is known to be 5%. Consider the following questions:
(a)
Obtain a PDE for a zerocoupon bond price with maturity
T
. Determine the solution to this
PDE (for this, you may use results presented on page 787 in the textbook).
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This note was uploaded on 01/11/2010 for the course ACTSC 446 taught by Professor Adam during the Fall '09 term at Waterloo.
 Fall '09
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