PSTAT 176/276 Assignment #4 Solutions
Problem 1 Consider a binomial tree with u = 1.1, d = 0.92, S0 = 20 and r = 0.04. The
physical probability is p = 0.5. We consider an exponential utility maximization problem. Let
U (x) = 2ex/2 .
that maximizes E[U (X

25.A Constructing the BDT Tree
Appendix 25.A CONSTRUCTING THE BDT TREE
In this appendix we verify that the tree in Figure 25.5 matches the price information in Table
25.1. We also see how to construct the tree. For reference, Figure 25.12 depicts the one-

1
Foundations
This chapters two parts develop key ideas from two elds, the intersection of
which is the topic of this book. Section 1.1 develops principles underlying the
use and analysis of Monte Carlo methods. It begins with a general description and si

6
Interest-Rate-Dependent Assets
6.1 Introduction
In this chapter, we develop a simple, binomial model for interest rates and
then examine some common assets whose value depends on interest rates.
Assets in this class are called fixed income assets.
The s

# Question 1
# the initial paramtre of call option
S0 <- 95
time <- 0.5
sigma <- 0.2
r <- 0.05
M <- 400 # 400 paths
dt <- time/(M) # delta t
Time <- seq(0, time, length.out = 401)
Time <- paste(rep('t=', 401), Time, seq = ")
set.seed(125) # random seed
S.

5
Portfolio Management
An investment in a risky security always carries the burden of possible losses
or poor performance. In this chapter we analyse the advantages of spreading
the investment among several securities. Even though the mathematical tools
i

108
3 Generating Sample Paths
3.3 Gaussian Short Rate Models
This section and the next develop methods for simulating some simple but
important stochastic interest rate models. These models posit the dynamics
of an instantaneous continuously compounded sh