September 1, 2004

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• September 1, 2004

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What is a derivative?

• Definition
• an agreement between two parties which has a
  value determined by the price of something else.
• Types
• Options, futures, and swaps
• Uses
• Risk management
• Speculation
• Reduce transaction costs
• Regulatory arbitrage

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Common Symbols
So Spot price at time 0 K Strike price t
Current time T Time at expiriation FO,T
Forward price at time 0, for maturity date, T ST
Spot price at expiration e exponential
(used for continuous compounding)
enr continuous compounding for n periods at r
interest rates n number of periods r
interest rate expected return E0
Expectation as of time 0 Lease Rate
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Three different perspectives

• End users
• Corporations
• Investment managers
• Investors

• Intermediaries
• Market-makers
• Traders

• Economic observers
• Regulators
• Researchers

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Financial engineering

• The construction of a financial product from
  other products
• New securities can be designed by using existing
  securities
• Financial engineering principles
• Facilitate hedging of existing positions
• Enable understanding of complex positions
• Allow for creation of customized products
• Render regulation less effective

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The role of financial markets

• Insurance companies and individual
  communities/families have traditionally helped
  each other to share risks
• Markets make risk-sharing more efficient
• Diversifiable risks vanish
• Non-diversifiable risks are reallocated
• Recent example Earthquake bonds by Walt Disney
  in Japan

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Exchange traded contracts

• Contracts proliferated in the last three decades
• What were the drivers behind this proliferation?

Table 1.1
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Increased volatility

• Oil prices 1951-1999

• DM/ rate 1951-1999

Fig. 1.1
Fig. 1.2
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led to new and big markets

• Exchange-traded derivatives
• Over-the-counter traded derivatives Even more!

Fig. 1.4
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Basic transactions

• Buying and selling a financial asset
• Brokers Commissions
• Market-makers Bid-ask (offer) spread
• Example Buy and sell 100 shares of XYZ
• XYZ bid 49.75, offer 50, commission 15
• Buy (100 x 50) 15 5,015
• Sell (100 x 49.75) - 15 4,960
• Transaction cost 5015 - 4,960 55

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Short-selling

• When price of an asset is expected to fall
• First borrow and sell an asset (get )
• Then buy back and return the asset (pay )
• If price fell in the mean time profit -
• The lender must be compensated for dividends
  received (lease-rate)
• Example Short-sell IBM stock for 90 days

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• Why short-sell?
• Speculation
• Financing
• Hedging
• Credit risk in short-selling
• Collateral and haircut
• Interest received from lender on collateral
• Scarcity decreases the interest rate
• Repo rate in bond markets
• Short rebate in the stock market

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Figure 2.1 Types of derivative markets
EXCHANGE TRADED Traded on exchanges (e.g.
LIFFE, CBOT, CME) Available for restricted set
of assets Fixed contract sizes and
settlement dates Easy to reverse the position
Credit risk eliminated by clearing house
margining system (marking to market)
OVER-THE-COUNTER Supplied by intermediaries
(banks) Customised to suit buyer Can be done
for any amount, any settlement date Credit
risk of counterparty and expensive to
unwind Allows anonymity - important for
large deals New contracts do not need
approval of regulator
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Figure 2.2 Financial futures markets
INSTRUMENTS Money Market Instruments 3
month Eurodollar deposit, 90 day US T-bills,
3 month Sterling or Euro deposits Bonds
US T-bond, German Bund Stock Indices
SP500, FTSE100 Currencies Euro, Sterling,
Yen, etc. Mortgage Pools (GNMA)
EXCHANGES CBOT CME NY Futures
Exchange Philadelphia Exchange (PHLX) Pacific
Stock Exchange (PSE) LIFFE (London) MATIF
(Paris) Eurex (Frankfurt) Singapore (SIMEX),
Hong Kong, Tokyo, Osaka Sydney Futures Exchange
(SFE)
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Figure 2.3 Speculation with futures
Profit per contract
Long future
10
F2 90
0
Futures price
F2 110
F1 100
-10
Short future
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Figure 2.4 Profit payoff (direction vectors)
Profit
Profit
1
-1
10
10
100
100
110
90
1
-1
Long Futures or Long Spot
Short Futures or Short Spot
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Figure 2.6 Arbitrage with futures
Stock price S 100 Safe rate r 4
p.a. Quoted futures price F 102 Strategy
today Sell futures contract at 102 (receive
nothing today) Borrow 100, but stock (
synthetic future) Use no own funds 3
months time (T 1/4) Loan outstanding
100 (10.04/4) 101 Deliver stocks and
receipts from F.C. 102 Riskless profit
1
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Figure 2.7 Backwardation and Contango
Forward price in contango F gt S
Stock price, St
0
T
At T, ST FT
Forward price in backwardation F lt S
For simplicity we assume that the spot price
remains constant. In practise, S and hence F
will fluctuate as you approach T but with Ft gt St
if the market is in contango and Ft lt St if the
market is in backwardation.
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Figure 2.8 Hedging using futures
Long Underlying Short Futures
1
- 1
0
Hedge

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Figure 2.9 Rolling over a futures contract
Short Sept. Future
Close out Sept. Future Buy March Future
Close out March Future Buy Sept. Future
Close out Sept. Future
April
June
Oct.
Dec.
April
June
Sept.
August
February
August
March
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Figure 2.10 Value of forward contract
New 3-month forward Ft 101.25
Initial 6-month forward F0 K 90
Value of initial 6-month forward Vt (Ft - F0)
e-r(T-t)
Both forward contracts expire
January
March
June
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Figure 1.1 Buy one European call option
Strike price K 80
Profit
5
K 80
0
88
83
ST
Call premium
-3
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Equation for a call option
Call profit max0,spot price at expiration -
strike price - future price of option premium
Example risk free rate 2, premium 93.81,
price at expiration 1,100
strike price 1,000.
1. Future value of premium 1.02 X 93.81
95.68 2. Max0, 1,100 - 1,000 - 95.68 4.32
Example risk free rate 2, premium 93.81,
price at expiration 900
strike price 1,000.
1. Future value of premium 95.68 2.
Max0,900-1000- 95.68 -95.68 (note
maximum loss is premium!)
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Figure 1.2 Sell (write) a European call option
Strike price K 80
Profit
3
Call premium
83
0
88
K 80
ST
-5
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Figure 1.3 Buy (long) a European put option
Strike price K 70
Profit
3
68
ST
0
65
K 70
Put premium
-2
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Figure 1.4 Sell (write) a European put option
Strike price K 70
Profit
2
Put premium
65
0
ST
68
K 70
-3
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Figure 1.5 Liabilities using swaps
Floating to Fixed Liability
Issue Floating Rate Bond
LIBOR 0.5
6 fixed
LIBOR
Firms Swap
Net Payment 0.5 6 6.5 (fixed)
Fixed to Floating Liability
Issue Fixed Rate Bond
6.2 fixed
LIBOR
6 fixed
Firms Swap
Net Payment 0.2 LIBOR (floating)
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Figure 1.6 Assets using swaps
Floating to Fixed Asset
Hold Floating Rate Bond
LIBOR - 0.5
6 fixed
LIBOR
Firms Swap
Net Receipts 6 - 0.5 5.5 (fixed)
Fixed to Floating Asset
Hold Fixed Rate Bond
5.7 fixed
LIBOR
6 fixed
Firms Swap
Net Receipts LIBOR - 0.3 (floating)
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Figure 1.7 Swap financial intermediary
Hold Floating Rate Bond
LIBOR - 1
12 fixed
Without swap if LIBOR gt 13 firms swap makes a
loss.
LIBOR
11 fixed
Firms Swap
After swap Net Receipts (12 - 11) LIBOR
- (LIBOR - 1) 2 (fixed)
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Figure 1.8 Leverage from option (Purchase 100
shares)
OPTIONS MARKET (JULY) Call premium, C
3 Premium paid 300 Strike price, K 80
CASH MARKET (JULY) Spot price, S 78 Cash paid
7800
OPTIONS MARKET (OCT.) Profit 8 (88 -
80) Net profit 800 - 300 Return 500/300
167
CASH MARKET (OCT.) Profit 10 (88 -
78) Total profit 1000 Return 1000/7800
12.8
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Appendix