STATS 461
Fall 2016
Homework Assignment #2
Due date: before class on Wednesday, 10/5
1. Normal and Lognormal Distributions.
(a) Suppose that the log return, is normally distributed with mean -0.0124 and standard deviation
0.0675, what is the mean and stan

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# Donskers Theorem #
#
n=500 # total number of steps in a random walk
t=0.3 # focus on t=0.3, based on the theorem, W_cfw_n,0.3 should converges to
Wiener process W(0.3)
sim=10000 # simulate 10000 random walk paths
W <- numeric(sim)
for ( i in 1:sim)cfw

STATS 461
Fall 2016
Homework Assignment #1
Due date: before class on Friday, 9/16.
Notes:
All tests are based on the 5% significance level.
R packages quantmod and fBasics are helpful in doing this assignment.
1. Suppose that X Bernoulli(p) with p 2 (0,

STATS 461
Fall 2016
Stochastic Process
1. Stochastic Process.
A stochastic process cfw_Xt is a collection cfw_Xt : t I of random variables where the index t
belongs to the index set I . Typically, I is an interval in R (in which case we say that cfw_Xt

Compounding
Money borrowing and lending involve interest. Interest rates
ordinary people work with are compounded annually,
semiannually, quarterly, monthly, weekly or daily.
Example: Suppose that $100 is invested for a year with interest rate 10%
annum.

# Payoff and profit of a call option from a long position at time of maturity
r <- 0.08 # interest rate
premium <- 3 # premium per share
T <- 0.5 # expiration date
K <- 25 # strike price
payoff <- function(x) sapply(x, function(x) max(c(x - K, 0)
profit <

One-step Binomial Tree
Suppose that a stock has price $100/share at current time and its
price at the end of one month will be either $90 (down state) or
$110 (up state). Assume that a call option exists on this stock.
The call option has a strike price o