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RMSC 2001 Exercise 2 Answer
1.
(a)
(b)
2.
(a)
(b)
(c)
(d)
(e)
The dollar you invest at time 1 = (10/1.2)*0.8*(0.9^0.5) = 6.324
The dollar will have accumulated by time 7 = 100/0.8/(0.9^0.5)*1.2 = 142.3
The accumulated value = 500 * (1+0.05/12)^(2*12) = 55
RMS 2001
Homework 4
Due date: 5pm, Apr 20 (Thursday). Assignment Box at LSB 1/F.
1. What is the price of a 5-year bond with face value 5000 and coupon rate 1%.
The bond yield is 3%.
2. Assume that the monthly interest rate is constant. On April 1st, the p
RMS 2001
Homework 3
Due date: 6pm, Mar 21 (Wednesday). Assignment Box at LSB 1/F.
1. The current price of stock S is So . For the same maturity time T , given
that c1 , c2 , c3 , c4 are the prices for call options 1,2,3,4, with strike price K =
20, 25, 30
RMS 2001
Homework 2
Due date: 5pm, Feb 22 (Wednesday). Assignment Box at LSB 1/F.
1. An insurance company has agreed to make payments to a worker age x who was
injured at work. The payments are 150,000 per year, paid annually, starting
immediately and con
RMS 2001
Homework 1
Due date: 5pm, Feb 1 (Wednesday). Assignment Box at LSB 1/F.
1. With respect to each of the following, indicate whether you would classify the
event or condition as a peril or a hazard: explosion, theft, lifting heavy objects
incorrect
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RMS 2001
Exercise 9
1. Your portfolio consists of two bonds: two units of North Korean(N.K.) government bonds and three units of Philippines(P.) government bonds. The face
values, the recovery rate and the probability of default for the two bonds are
resp
Question 1
(a)
Probability Model
CL = 2=1 bi CEi (1 fi )
i
= bN K CEN K (1 fN K ) + bP CEP (1 fP )
where bN K Bernourlli(pN K = 0.1), CEN K = 2 1000 = 2000, fN K = 0.2, bP
Bernourlli(pP = 0.08), CEP = 3 500 = 1500, fP = 0.3.
(b)
E (CL) = pN K CEN K (1 fN
RMS 2001
Exercise 8
1. The below is the history of Stock A. You are holding 1000 shares of stock A.
Day
1
2
3
4
5
6
7
8
Stock price
40
40.3
39.8
38.2
39.5
37.3
37.3
41.1
(a) Find the volatility of Stock A.
(b) Using normal approximation, nd the ve days 1%
RMS 2001
Exercise 7
1. What is the price of a 10-year zero coupon bond with face value 10000 when
the interest rate is 3%?
2. What is the price of a 5-year 6% coupon rate bond with face value 20000
when the interest rate is 2%? (Assuming coupon is also pa
RMS 2001
Exercise 6
1. Suppose your company is involved in a margin buying of 20000 shares of a stock of value
$ 40 per share. 90 % of the total value is borrowed from the bank while the rest are
investment from your company. The maintenance margin requir
RMS 2001
Exercise 5
1. Suppose the spot price (current stock price) be 98. The below are some
European options that you nd in the market:
Option Number
1
2
3
4
5
Type
Call
Put
Put
Call
Call
Strike price
100
100
95
105
95
option price Maturity
3
3 months
4
RMS 2001
Exercise 4
1. Given the extra life time of a 80-year-old follows uniform distribution
[0, 10]. Find
2 p80 .
q85 .
3 p84 q87 .
2. A 3-year life annuity on a 30-year-old provides for annuity benets of 1
at time 0, 2 at time 1 and 4 at time 2. Yo
RMS 2001
Exercise 3
1. Given q60 = 0.2, q61 = 0.25, q62 = 0.25, q63 = 0.3, q64 = 0.4.
a) Find lx for ages 60 to 65, beginning with l60 = 1000.
b) Find the probability that i) a 61-year-old will die between the ages
62 and 64. ii) a 62-year-old will live t
RMS 2001
Exercise 2
1. The discount factor from time 2 to 0 is 0.9, from time 5 to 2 is 0.8. The
accumulated value from time 5 to 7 is 1.2.
a) How much must you invest at time 1, in order to accumulate 10 at
time 7?
b) If you invest 100 at time 1, how muc
RMS 2001
Exercise 1
1. With respect to each of the following, indicate whether you would classify
the event or condition as a peril or a hazard: Typhoon, obesity, sickness,
anxiety, bird u, carelessness.
2. With respect to each of the following, classify
RMS 2001
Exercise 6
1. Suppose your company is involved in a margin buying of 20000 shares of a stock of value
$ 40 per share. 90 % of the total value is borrowed from the bank while the rest are
investment from your company. The maintenance margin requir
Chapter 7
Introduction to Credit Risk Management
Financial Risk Management
Market Risk
Credit Risk
borrower does not make payment as promised
Operational Risk
The risk of change in value of the investment/trading
portfolio
Risk arising from people/systems
Chapter 6
Introduction to Market Risk Management
Financial Risk Management
Market Risk
Credit Risk
Borrower does not make payment as promised
Operational Risk
The risk of change in value of the investment/trading
portfolio
Risk arising from people/systems
Chapter 5
Introduction to Financial instruments
5.1 Introduction
Securities () = all financial instruments
Assets/ Equities ()
Commodities ()
Stocks() ownership of the firm
e.g. oil, gold, silver
Debts ()
Bonds() lend money to the firm
5.1 Introduction
Fi
Chapter 4
Loss distribution
Loss distribution
Life () insurance (Protection against life)
Payment depends on the life time of individuals
Need to know the probability distribution of
death benefits determined
Life time - random
the length of life time
Cas
Chapter 3
Life Insurance
Life Table = Mortality table
Notation
lx=number
Basic Relationship
of people alive at age x
dx=number of people die b/w age x and x+1
lx+1=lx-dx
Life/Mortality table
X
lx
dx
0
100,000
2000
1
98,000
1500
2
96,500
1000
3
95,500
900