MA4269 Tutorial 1 Solution
Question 1. Suppose the current forward price for a 6-month forward contract is $35, and the
underlying non-dividend paying stock is currently at $30. Suppose the risk-free
MA4269 Tutorial 1 (Week 3)
Question 1. Suppose the current forward price for a 6-month forward contract is $35, and the
underlying non-dividend paying stock is currently at $30. Suppose the risk-free
MA4269 Tutorial 3 Solution
Question 1. Consider the Brownian motion Wt , t
0. Show that for any s, t
0, we have
Cov [Wt , Ws ] = mincfw_s, t.
Here Cov[X, Y ] is the covariance between X and Y .
Soluti
MA4269 Tutorial 3 (Week 5)
Question 1. Consider the Brownian motion Wt , t 0. Show that for any s, t 0, we have
Cov [Wt , Ws ] = mincfw_s, t.
Here Cov[X, Y ] is the covariance between X and Y .
Questi
MA4269 Assignment 3 (2 Questions)
Important: due on Wednesday 19 October 2016. Submit to the boxes in
the front of LT33 before the beginning of the lecture, according to your
tutorial group number.
Pl
MA4269 Semester 1 AY 2017/18
Final Exam Information
Date: 06/12/2017
Time: 5:00 PM
Venue: MPSH5
1. It is a closed book exam. You are allowed to bring TWO(2) pieces of A4 size, double
sided help sheets
MA4269 Tutorial 8 Solution
Oct, 2017
MA4269 Tutorial 8 Solution
Oct, 2017
1/8
Review
(1) Binomial tree model for American put option:
maxcfw_(K S)+ , p (K Su)+ + (1 p )(K Sd)+ .
(2) Linear Complementa
MA4269 Tutorial 6 Solution
Question 1. Suppose that the price processes for two tradable non-dividend paying assets St
and Qt are given by
dSt = St dt + St dWt ,
dQt = Qt dt + Qt dWt
where , , > 0, >
Chapter 6
Barrier options
1
Introduction
One of the most commonly traded path-dependent options is the continuous barrier
option. This is an option with the ordinary call/put payoff subject to an addi
MA4269 Tutorial 8 Solution
Question 1. Assume no dividends. Let C(S, t) and (P (S, t) denote the time-t price of an
American call and American put options respectively with the same maturity date T an
MA4269 Tutorial 8 (Week 10)
Question 1. Assume no dividends. Let C(S, t) and (P (S, t) denote the time-t price of an
American call and American put options respectively with the same maturity date T a
MA4269 Assignment 3 Solution
(2 Questions, Total 30 Marks)
Question 1. Suppose we are in the Black-Scholes framework and that r = 0 so that
the stock price dynamics, under the risk-neutral measure Q,
MA4269 Assignment 1 Solution
(4 Questions, Total 40 Marks)
Question 1. Let c and p denote the call and put price (premiums) today with the
same strike price K respectively. Let F0,T be the forward pri
MA4269 Assignment 2 Solution
(2 Question, Total 20 Marks)
Question 1. Suppose that a stock price St follows geometric Brownian motion with
expected rate of return and volatility :
dSt = St dt + St dWt
MA4269 Tutorial 6 (Week 8)
Question 1. Suppose that the price processes for two tradable non-dividend paying assets St
and Qt are given by
dSt = St dt + St dWt ,
dQt = Qt dt + Qt dWt
where , , > 0, >
MA4269 Tutorial 10 (Week 12)
1
Asian options
Question 1. Let At be the running arithmetic average of the underlying stock price St defined
by
Z
1 t
Su du.
At =
t 0
Consider a European arithmetic float
MA4269 Assignment 3 Hints
(2 Questions, Total 30 Marks)
Question 1. Suppose we are in the Black-Scholes framework and that r = 0 so that
the stock price dynamics, under the risk-neutral measure Q, is
MA4269 Assignment 4 (2 Questions)
TOTAL = 20 MARKS
Question 1. Suppose the current (non-dividend paying) stock price is S0 = S and
S > B > K. Show that under the risk-neutral measure Q,
Q
min St B, ST
MA4269 Tutorial 6 Solution
Oct, 2017
MA4269 Tutorial 6 Solution
Oct, 2017
1 / 12
Review
(1) Generalized Girsanov Theorem: If Wt is a standard BM under P, then
R
ft = Wt + t (s)ds is a standard BM unde
MA4269 Tutorial 9 Solution
For this tutorial, please refer to the appendix below for unexplained terms and results that you
may need.
Question 1. Formulate the PDE pricing model for the European down-
MA4269 Tutorial 5 Solution
Question 1. Determine
c
, the rate of change of the value of the European call option relative
q
to the dividend yield.
Solution. Recall from previous tutorial that
St N 0 (
MA4269 Tutorial 4 Solution
Question 1. What is the Black-Scholes price of a European put option on a non-dividend
paying stock when the stock price is $69, the strike price is $70, the risk-free inter
MA4269 Tutorial 5 (Week 7)
Question 1. Determine
c
, the rate of change of the value of the European call option relative
q
to the dividend yield.
Question 2. Does dividend yield increase or decrease
MA4269 Tutorial 4 (Week 6)
Question 1. What is the Black-Scholes price of a European put option on a non-dividend
paying stock when the stock price is $69, the strike price is $70, the risk-free inter
Two Assets Options
Exam Info
Revision
Sample Questions
Mathematical Finance II
Chao ZHOU
Department of Mathematics, NUS
[email protected] nus.edu.sg
11th Lecture, 15 November 2017
Chao ZHOU
NUS
MA4269
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