Semester I, 2013: MAL732
Practice Problems Sheet 7: Bonds and Interest Rates
1. A 1-year ZCB with face value Rs 100 is currently selling for Rs 85. What is the interest rate after 6 months
if the investment for 6 months in zero coupon bonds gives a contin
Semester I, 2013: MAL732
Practice Problems Sheet 4: The Greeks
1. The Black-Scholes price for a certain European call option on stock is Rs 50. The stock is currently trading for
Rs 1000 per share, and it is known that Rs 452 must be borrowed in the repli
Semester I, 2013: MAL732
Practice Problems Sheet 6: CAPM and SML
1. You owns two risky assets, both of which plot on the security market line. Asset A has an expected return of 12% and beta
of 0.8. Asset B has an expected return of 18% and a beta of 1.4.
MAL 732: Financial Mathematics
Problem Sheet 5: Portfolio Optimization
1. Suppose there are three nancial market scenarios = cfw_w1 , w2 , w3 with dierent probabilities of occurrence. Consider the following table showing the returns on two dierent stocks
Semester I, 2013; MAL732: Practice Problems Sheet 3
Binomial Model and Black-Scholes Model
Answers
1. Let the current stock price be 120 and there are only two possibilities of its change: go up by 25%
with probability 70% or down by 20%. Assume the risk
Semester I 2013; MAL732: Practice Problems
1. If you wish to accumulate Rs 140,000 in 10 years, how much must you deposit today in an account
that pays an annual interest rate of 8%?
(A: Rs 64847)
2. At what annual interest rate must Rs 137,000 be investe
IEOR 6711: Stochastic Models I SOLUTIONS to Second Midterm Exam, Chs. 3-4, November 20, 2007
Justify your answers; show your work. 1. Selling Flour: The Grainery. (30 points) The Grainery is a store that sells flour to bakers. Suppose that bakers come to
IEOR 6711: Stochastic Models I Second Midterm Exam, Chapters 3 and 4, November 20, 2007
Justify your answers; show your work. 1. Selling Flour: The Grainery. (30 points) The Grainery is a store that sells flour to bakers. Suppose that bakers come to the G
IEOR 6711: Stochastic Models I Second Midterm Exam, Chapters 3-4, November 18, 2012 SOLUTIONS
Justify your answers; show your work. 1. Forecasting the Weather (12 points) Consider the following probability model of the weather over successive days. First,
IEOR 6711: Stochastic Models I Second Midterm Exam, Chapters 3-4, November 18, 2012 There are four questions, each with multiple parts.
Justify your answers; show your work. 1. Forecasting the Weather (12 points) Consider the following probability model o
IEOR 6711: Stochastic Models I Second Midterm Exam, Chapters 3 & 4, November 21, 2010 SOLUTIONS
Justify your answers; show your work. 1. Random Walk on a Graph (25 points)
Random Walk on a Graph
C A 2
E 5 1 D
2 3 G 1 F
1 B
3
Figure 1: A random walk on a g
IEOR 6711: Stochastic Models I Second Midterm Exam, Chapters 3 & 4, November 21, 2010
Justify your answers; show your work. 1. Random Walk on a Graph (25 points)
Random Walk on a Graph
C A 2
E 5 1 D
2 3 G 1 F
1 B
3
Figure 1: A random walk on a graph. Cons
SOLUTIONS to the First Midterm Exam, October 7, 2012 IEOR 6711: Stochastic Models I,
1. Poisson Process and Transforms (30 points) [grading scheme: On all questions, partial credit will be given. Up to 4 points off for errors on parts (a)-(g); up to 8 poi
IEOR 6711: Stochastic Models I SOLUTIONS to First Midterm Exam, October 10, 2010
Justify your answers; show your work. 1. Exponential Random Variables (23 points) Let X1 and X2 be independent exponential random variables with means E[X1 ] 1/1 and E[X2 ] 1
IEOR 6711: Stochastic Models I First Midterm Exam, Chapters 1-2, October 10, 2010
Justify your answers; show your work. 1. Exponential Random Variables (23 points) Let X1 and X2 be independent exponential random variables with means E[X1 ] 1/1 and E[X2 ]
IEOR 6711: Stochastic Models I First Midterm Exam, Chapters 1-2, October 7, 2008
Justify your answers; show your work. 1. A sequence of Events. (10 points) Let cfw_Bn : n 1 be a sequence of events in a probability space (, F, P ). (a) Explain what that me
15-859M: Randomized Algorithms Lec 8: Balls and Bins/Two Choices
Anupam Gupta February 2, 2011
1
Balls and Bins
The setting is simple: n balls, n bins. When you consider a ball, you pick a bin independently and uniformly at random, and add the ball to tha
Answers to the exam ISP of December 19, 2005 1. Counting time in hours: a. Taking t = 2 in P (N(t) = 20) = e-10t (10t)2 0/20! yields 0.089 b. P (N(0.01) 1) = 1 - e-0.1 , or P (X 0.01) where X is an interarrival time, hence exponentially distributed with p
Examination Introduction to Stochastic Processes (LNMB/Dutch Master Program) Monday December 19, 2005, 12.00 - 15.00 hours This exam consists of 5 problems Use of book is not permitted Motivate your answers! 1. Suppose that print jobs arrive at a network
LNMB EXAM Introduction to Stochastic Processes (ISP) Saturday October 7, 2006, 11.00-14.00 hours. The exam consists of five exercises, each with several parts. For each part it is indicated between square brackets how many points can be earned for the ite
IEOR 6711: Stochastic Models, I Fall 2012, Professor Whitt, Final Exam SOLUTIONS
There are four questions, each with several parts. 1. Customers Coming to an Automatic Teller Machine (ATM) (30 points) Customers arrive one at a time at a single automatic t
IEOR 6711: Stochastic Models, I Fall 2012, Professor Whitt, Final Exam
There are four questions, each with several parts. 1. Customers Coming to an Automatic Teller Machine (ATM) (30 points) Customers arrive one at a time at a single automatic teller mach
IEOR 6711: Stochastic Models, I Fall 2010, Professor Whitt, Final Exam SOLUTIONS
There are four questions, each with several parts. Question 2 is longer than the others and thus counts more. 1. The Eight (8) Subway Line. A new subway line has been added t
IEOR 6711: Stochastic Models, I Fall 2010, Professor Whitt, Final Exam
There are four questions, each with several parts. Questions 2 and 4 are longer than the others and thus count more. 1. The Eight (8) Subway Line. (20 points) A new subway line has bee
IEOR 6711: Stochastic Models, I Fall 2008, Professor Whitt, Final Exam
There are three questions, each with several parts. 1. The BAD Lunch Deli (40 points) Santiago Balsero, Andrew Ahn and Zuxuan Deng have joined forces to form their own delicatessen, th
IEOR 6711: Stochastic Models, I: Final Exam Fall 2007, SOLUTION NOTES
1. The GIN Barbershop (20 points) Ioannis Giannakakis, Gisli Ingimundarson and Behzad Nouri have joined together to form the GIN barbershop. The GIN barbershop has room for at most five