QF3101 Investment Instruments:
Theory and Computation
Module Information
Gong Zheng
Department of Mathematics
National University of Singapore
1/8
Lecturer: Dr. Gong Zheng
Office hours: By appointment via matgz@nus.edu.sg
Office: S17-05-19
Course material

QF3101 Investment Instruments: Theory and Computation
Semester 2, 2015/2016
Tutorial 4 Solution
1. (i)
The July 2015 contract has the expiry date of 14 July 2015, this date occurs after the
commitment date of 10 July and nearest to it (comparing against f

QF3101 Investment Instruments: Theory and Computation
Semester 2, 2015/2016
Tutorial 11
1.
Consider a portfolio of two assets with weight vector w = (w1 , w2 ) and total portfolio value
of W . Rates of return of the two assets are correlated with a correl

QF3101 Investment Instruments: Theory and Computation
Semester 2, 2015/2016
Tutorial 10
1.
Assume that there are 250 trading days in a year and rates of returns mentioned below are
normally distributed.
(a)
Consider $10 million invested in a stock. The an

QF3101 Investment Instruments: Theory and Computation
Semester 2, 2015/2016
Tutorial 2 Solution
1.
Storage cost is USD 2/4=USD 0.5 per ounce per quarter.
Quarterly interest rate is 1%/4=0.25%.
The theoretical forward price is
4
2
3
4
F = 1664(1.0025) + 0.

QF3101 Investment Instruments: Theory and Computation
Semester 2, 2015/2016
Tutorial 1
1.
Recall that a bond with face value F , annual coupons at rate c, n years to maturity, and the
yield to maturity (annualized) y, has its valuation given by the formul

QF3101 Investment Instruments: Theory and Computation
Semester 2, 2015/2016
Tutorial 8 Solution
1. (i) The fair fixed rate for the 3 6 is the forward rate for the 3-month period 3 months from
now:
1 + 0.3971% 182/360
360
f=
1
= 0.5302%.
1 + 0.2636% 91/36

QF3101 Investment Instruments: Theory and Computation
Semester 2, 2015/2016
Tutorial 3 Solution
1.
Case 1. At time 0, obtain a forward contract to sell one unit of the stock at time T at price
F0 , and borrow S0 cash to buy one unit of the stock. At time

QF3101 Investment Instruments: Theory and Computation
Semester 2, 2015/2016
Tutorial 7 Solution
1.
Let the implied rate over the 9-month period be x.
Then we have
(1 + 0.405%
92
91
90
)(1 + 0.6%
)(1 + 0.825%
)=1+x
360
360
360
which yields x = 0.4621%.

QF3101 Investment Instruments: Theory and Computation
Semester 2, 2015/2016
Tutorial 3
1.
Time now is 0 and a forward contract on a dividend-paying stock expires at time T . The
current stock price is S0 and the dividend of $D is paid at time t, 0 < t < T

QF3101 Investment Instruments: Theory and Computation
Semester 2, 2015/2016
Tutorial 6 Solution
1. (i)
(ii)
Since you do not wish to wait in the bid-ask queue, you sell the T-bill at the bid quote
of 1.84. With a maturity of 38 days and a bid quote of 1.8

QF3101 Investment Instruments: Theory and Computation
Semester 2, 2015/2016
Tutorial 5 Solution
1.
In 4 months, 0.5 0.12 $100 million = $6 million will be received and 0.5 0.096
$100 million = $4.8 million will be paid. In 10 months, $6 million will be r

QF3101 Investment Instruments: Theory and Computation
Semester 2, 2015/2016
Tutorial 9 Solution
1.
Let c = c/d(0, T ), S0 = S0 /d(0, T ).
ST
ST X
ST > X
Short Call
value
profit
0
c
(ST X)
c (ST X)
Long Asset
value
profit
ST
ST S0
ST
ST S0
Total Profit
ST

QF3101 Investment Instruments: Theory and Computation
Semester 2, 2015/2016
Tutorial 11 Solution
1.
Note that for delta-normal methods, the individual VaR is given by
VaRi =
i Wi
=
i wi W;
i = 1; 2:
Hence multiplying both sides of the equation
2
p
= w12
2

QF3101 Investment Instruments:
Theory and Computation
Chapter 6
Value at Risk
Gong Zheng
Department of Mathematics
National University of Singapore
1/71
Outline
1
VaR basics
2
Valuation approaches
3
Delta-Normal Methods
4
Simulation Methods
5
Risk mapping

QF3101 Investment Instruments:
Theory and Computation
Chapter 4
Forward and Futures Examples
Gong Zheng
Department of Mathematics
National University of Singapore
1/79
Outline
1
Fixed income instruments
2
Interest rate contracts
3
Currency contracts
2/79

QF3101 Investment Instruments:
Theory and Computation
Chapter 1
Visual Basic for Applications
Gong Zheng
Department of Mathematics
National University of Singapore
1/34
What is VBA?
Visual Basic for Applications (VBA) is the language embedded
within the s

QF3101 Investment Instruments:
Theory and Computation
Chapter 2
Forward, Futures and Hedging
Gong Zheng
Department of Mathematics
National University of Singapore
1/96
Outline
1
Forward contracts
2
Futures contracts
3
Hedging using forward/futures
4
Minim

QF3101 Investment Instruments:
Theory and Computation
Chapter 3
Swaps
Gong Zheng
Department of Mathematics
National University of Singapore
1/51
Swaps
A swap is an agreement between two counter-parties to
exchange cash flows in the future according to a p

QF3101 Investment Instruments:
Theory and Computation
Chapter 5
Options
Gong Zheng
Department of Mathematics
National University of Singapore
1/69
Outline
1
Introduction
2
Trading Strategies
3
Fixed income and interest rate options
2/69
Outline
1
Introduc

Midterm review
Forward price: assuming we are now at time 0, then F0 is the fair price you should pay in
future (say time T ) based on the time 0 value of the underlying.
If the time 0 value of the asset is S0 , and it pays known income Ii at time i and

QF3101 Investment Instruments: Theory and Computation
Semester 2, 2015/2016
Tutorial 9
1.
Consider the trading strategy of writing a covered call. Suppose at time 0, one unit of asset
A is purchased at the price of S0 , and one call option (on one unit of

QF3101 Investment Instruments: Theory and Computation
Semester 2, 2015/2016
Tutorial 6
1.
2.
3.
A Treasury bill maturing in 38 days is quoted at a bid of 1.84 and an ask of 1.83. Assume
that you do not wish to spend time waiting in the bid-ask queue.
(i)

QF3101 Investment Instruments: Theory and Computation
Semester 2, 2015/2016
Tutorial 8
1.
Spot LIBORs (quoted using actual/360 convention) for a number of maturities are given in
the following table:
Maturity, months (days)
3 (91)
6 (182)
9 (274)
12 (365)

QF3101 Investment Instruments: Theory and Computation
Semester 2, 2015/2016
Tutorial 2
1.
The current price of gold is US$1664 per ounce. The storage cost is US$2 per ounce per year,
and is to be paid quarterly at the beginning of each quarter. Assuming a

QF3101 Investment Instruments: Theory and Computation
Semester 2, 2015/2016
Tutorial 1 Solution
1.
Function MyBondPrice(F, c, n, y) As Currency
Dim i As Integer
Dim temp As Currency
temp = 0
For i = 1 To n incrementally add the discounted coupons
temp = t

QF3101 Investment Instruments: Theory and Computation
Semester 2, 2015/2016
Tutorial 10 Solution
1. (a)
(b)
2.
The 1-day 99% VaR for the stock is
p
VaR = 2.326 0.25 1/250 $10 millon = $0.3678 millon.
Note that there are 5 trading days in a one-week period

QF3101 Investment Instruments: Theory and Computation
Semester 2, 2015/2016
Tutorial 5
1.
A $100 million interest rate swap has a remaining life of 10 months. Under the terms of
the swap, six-month LIBOR is exchanged for 12% per annum (compounded semiannu