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
# 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)
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%
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
Homework Assignment #1
Due date: before class on Friday, 9/16.
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,
# 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
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
FIN 300 and Your Texas Instruments BA II Plus: Set Up
The BA II Plus makes solving time value of money problems much simpler because it contains most of
the equations, that look fairly daunting, in its memory. To successfully use the BAII you need to set