Financial Products and How
They Are Used for Hedging
Chapter 2
Risk Management and Financial Institutions, Chapter 2 , Copyright John C. Hull 2006
2.1
Financial Markets
Exchange traded
Traditionally exchanges have used the openoutcry system, but increasin
RMS 2001
Chapter 6
Introduction to Financial Derivatives
6.1 Introduction
There are two classes of securities or instruments in the nancial marketplace, they are
Fundamental stocks and bonds
Stocks rights of ownership of the rm.
Bonds the rst claim on
RMS 2001 Introduction to Risk Management
Tutorial 1
1
Type of Risk
Objective risk: relative variation of the actual loss from expected loss.
Example: 10,000 houses were insured, on average 1% (100 houses) burn each year. Of course,
it is unlikely that ex
RMSC2001 Tutorial 2
Law of total probabilities: Let F1 , F2 , ., Fn be a sequence of events, forming a partition
over the sample space , i.e. Fi Fj = i = j (mutually exclusive) and n=1 Fi =
i
(collectively exhaustive). Then
For any event G, P (G) = n=1 P
RMSC2001 Tutorial 4
Probability axioms: Let be the sample space, F be the event space and P be the
probability measure. Then we have the following axioms:
1. P (E ) 0 E F
2. P () = 1
+
3. P
+
Ei
i=1
P (Ei ), where Ei F i, Ei Ej = , i = j
=
i=1
Set operato
RMSC2001 Tutorial 3
Payo Diagram and Prot Diagram
Payo: The value of the nancial derivative at maturity
Prot: Subtracted the initial cost from the payo
The payo diagram usually put the payo in the y -axis and put the underlying asset price
at maturity in
RMSC2001 Tutorial 5
Assumptions:
All assets/derivatives are liquid
There is no bid-ask spread
There is no transaction cost
There is no credit risk/counter-party risk
You are allowed to take the short position
You do not need to have margin/deposit f
RMSC2001 Tutorial 6
Let F (t) be the value of the forward contract at time t. At the maturity T , we have
F (T ) = S (T ) K
Using the argument from replicating portfolio,
F (t) = S (t) K (1 + r)(T t) t [0, T ]
If we set the initial value = 0, then
F (0) =
RMSC2001 Tutorial 7
Some terminologies for the moneyness of the options:
Intrinsic value: The value you get if you immediately exercise the option.
For example, at time t < T , the intrinsic value of
the European call option = maxcfw_S (t) K, 0
the Euro
RMSC2001 Tutorial 8
Using Multi-period Binomial Tree:
Each node will produce exactly 2 branches, indicating the 2 possibilities of the stock (underlying
asset of the derivative) price movement in the next period.
We need to build the tree until we match
RMSC2001 Tutorial 9
Let X be the terminal prot/loss after a specic target time horizon. Specically, X < 0 will indicate a
loss; and the amount/magnitude of loss will be usually reported as a positive number.
Recall the denition of the cumulative distribut
RMSC2001 Tutorial 11
Reminders on the optimal hedging:
Suppose you observed the historical prices cfw_S0 , S1 , ., ST and cfw_F0 , F1 , ., FT . To estimate
2
2
F = V ar[F ], S = V ar[S ], S,F = Cov [S, F ], rst you need to dierence the series
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How Traders Manage
Their Exposures
Chapter 3
Risk Management and Financial Institutions, Chapter 3 , Copyright John C. Hull 2006
3.1
A Traders Gold Portfolio. How Should
Risks Be Hedged? (Table 3.1, page 56)
Position
Spot Gold
Forward Contracts
Futures Co
Interest Rate Risk
Chapter 4
Risk Management and Financial Institutions, Chapter 4 , Copyright John C. Hull 2006
4.1
Measuring Interest Rates
The
compounding frequency used
for an interest rate is the unit of
measurement
The difference between quarterly
Volatility
Chapter 5
Risk Management and Financial Institutions, Chapter 5 , Copyright John C. Hull 2006
5.1
Background
The volatility of a variable is the standard
deviation of its return with the return being
expressed with continuous compounding
The v
Bank Regulation and
Basel II
Chapter 7
Risk Management and Financial Institutions, Chapter 7 , Copyright John C. Hull 2006
7.1
History of Bank Regulation
Pre-1988
1988:
BIS Accord (Basel I)
1996: Amendment to BIS Accord
1999: Basel II first proposed
R
The VaR Measure
Chapter 8
Risk Management and Financial Institutions, Chapter 8 , Copyright John C. Hull 2006
8.1
The Question Being Asked in VaR
What loss level is such that we are X%
confident it will not be exceeded in N
business days?
Risk Management
Market Risk VaR:
Historical Simulation
Approach
Chapter 9
Risk Management and Financial Institutions, Chapter 9 , Copyright John C. Hull 2006
9.1
Historical Simulation
(See Table 9.1 and 9.2)
Collect data on the daily movements in all
market variables.
T
Market Risk VaR:
Model-Building
Approach
Chapter 10
Risk Management and Financial Institutions, Chapter 10 , Copyright John C. Hull 2006
10.1
The Model-Building Approach
The main alternative to historical simulation is to
make assumptions about the probab
Correlations and
Copulas
Chapter 6
Risk Management and Financial Institutions, Chapter 6 , Copyright John C. Hull 2006
6.1
Coefficient of Correlation
The
coefficient of correlation between two
variables V1 and V2 is defined as
E (V1V2 ) E (V1 ) E (V2 )
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RMSC2001 Tutorial 10
We introduce two approaches to give the risk measure: Value at Risk,
given a holding period and a condence level that we prespecied
Parametric approach: Normal VaR
St St1
2
Let Rt =
be the daily return (which has no unit), with E [Rt