550.444
Introduction to
Financial Derivatives
Introduction
Weeks of September 4 and
September 9, 2013
1.1
Principals

David R Audley, Ph.D.; Sr. Lecturer in AMS
 david.audley@jhu.edu
 Office: WH 212A; 410-516-7136
 Office Hours: 4:30 – 5:30 Monday

Teaching Assistant(s)
 Huang, Qiushun (qhuang13@jhu.edu)
 Office Hours: Friday 4pm – 6pm
 Ward, Brian (bward16@jhu.edu)
 Office Hours: Monday & Wednesday 2pm – 3 pm
1.2
Schedule

Lecture Encounters
 Monday & Wednesday, 3:00 - 4:15pm,
 Mergenthaler 111

Section
 Section 1: Friday 3:00 - 3:50pm, Hodson 211
 Section 2: Thursday 3:00 - 3:50pm, WH 304
1.3
Protocol

Attendance
 Lecture – Mandatory (default) for MSE Fin
Math majors
 Quizzes & Clickers
 Section – Strongly Advised/Recommended

Assignments
 Due as Scheduled (for full credit)
 Must be handed in to avoid “incomplete”

Exceptions must be requested in advance
1.4
Resources

Textbook
 John C Hull: Options, Futures, and Other
Derivatives, Prentice-Hall 2012 (8e)
 Recommended: Student Solutions Manual
 On Reserve in Library
 Text Resources
 http://www.rotman.utoronto.ca/~hull/ofod/Errata8e/index.html
 http://www.rotman.utoronto.ca/~hull/TechnicalNotes/index.html
1.5
Resources

Supplemental Material
 As directed

AMS Website
 http://jesse.ams.jhu.edu/~daudley/444
 Additional Subject Material
 Class Resources & Lecture Slides
 Industry & Street “Research” (Optional)
 Consult at your leisure/risk
 Interest can generate Special Topics sessions

Blackboard
1.6
Measures of Performance



Mid Term Exam (~1/3 of grade)
Final Exam (~1/3 of grade)
Home work as assigned and designated
and Quizzes (~1/3 of grade)
1.7
Assignment

Thru week of Sept 9 (Next Week)
 Read: Hull Chapter 1 (Introduction)
 Read: Hull Chapter 2 (Futures Markets)
 Problems (Due September 16)
 Chapter 1: 17, 18, 22, 23; 34, 35
 Chapter 1 (7e): 17, 18, 22, 23; 30, 31
 Chapter 2: 15,16, 21, 22; 30
 Chapter 2 (7e): 15, 16, 21, 22; 27
1.8
Assignment

For week of Sept 16 (in 2 Weeks)
 Read: Hull Chapters 3 (Hedging with Futures)
 Problems (Due September 23)
 Chapter 3: 4, 7, 10, 17, 18, 20, 22; 26
 Chapter 3 (7e): 4, 7, 10, 17, 18, 20, 22; 26
1.9
Assets and Cash

Stock, Bond, Commodity, … (Assets)
 Risk vs. Return (Expected Return)

Cash (or Currency)
 Held, on Deposit or Borrowed

Terminology
 Assets – things we “own” (long)
 Liabilities – what we “owe” (short)
1.10
How Things Work


True Assets – A house, a company, oil, …
Ownership rights, contracts, & other legal
instruments which represent the true asset
 For us, many are indistinguishable from the
asset; are the asset
 Provide properties that can be quantified,
assigned, subordinated and made contingent
 Can be modeled
1.11
Who Makes it Work

Investment Banks: Capital Intermediation
 Companies into Stock
 Borrowings into Bonds

Broker-Dealers & Markets (Exchanges)
 Create everything else
 Facilitate transfer/exchange (trading)


Investors
Under the Watchful Eyes of Regulators,
Professional Associations and the Rule of Law
1.12
Creation & Exchange of Securities
and Instruments
Secondary Issues
Collateral
Create
Securities
Make
Markets
New Issue
Securities
Investment Banking
Broker-Dealers &
Exchanges
Securities &
Contracts
Manage
Invested
Funds
Institutional Investors
1.13
Two Fundamental Ideas in
Modeling
LOAN FROM STANDPOINT
OF LENDER

Cash Flow
Repayment of Loan
w/Interest at t0+T
Receive
 Cash flow diagram
 Receive vs. Pay over Time
t, time
Pay
Amount of Loan, t0

Payoff Cashflow
Gain
 Payoff diagram
S, Price
 Gain vs. Loss against Price
 Cashflows can depend
on some other variable
K
Loss
LONG STOCK AT
PRICE K
1.14
Real World Situation - Cash


Japanese Bank; borrow US dollars (USD)
to loan to its customers; term, 3 months
Go to Euromarket where it might be able
to get an Interbank Loan
Receive
(Borrow)
T = 1/4 year
Lt0 = 3 month interest rate in
effect at t0
USD
t0 + T
Borrow: USD
Pay Back: USD x (1 + Lt0 x T)
t0
Pay Back
USD+Lt0x(.25)xUSD
1.15
Real World Situation - Cash


What if Bank did not have credit line?
Could perform the same transaction as a
Synthetic in the FX and domestic Yen mkt
 Borrow Yen in local mkt for term T, at L(t0,Y)
 Sell Yen and buy USD in spot FX mkt at e(t0,Y)
 Finally, the bank buys Yen and sells USD in
the forward FX market for delivery at t0+T
1.16
Real World Situation - Cash

Cash Flows are Additive
Borrow Y for T
Y
USD
Yx(1+L(t0,Y)xT)
+
Buy USD sell Y at e(t0,Y)
Y = e(t0,Y) x USD
Y
+
Yx(1+L(t0,Y)xT)
USDx(1+L(t0,$)xT)
=
USD
Buy Y forward for t0+T
Y x (1 + L(t0,Y)xT)
= f(t0,T;Y) x USD1
USD1
= USD x (1 + L(t0,$) x T)
USDx(1+L(t0,$)xT)
t0
t0+T
1.17
Real World Situation - Cash

What’s the difference; what’s interesting
 International Banks have credit risk in the USD loan
 For the synthetic, the International Bank exposure is in
the forward contract only
 No principal risk
 Yen loan default is a domestic issue (central bank)
 The synthetic can be used to price the derivative, excredit risk (what’s the derivative in this example?)
 Each side could be the other’s hedge
 Different markets involve many legal & regulatory
differences
1.18
Real World Situation - Tax

Situation:
 In Sept ‘02, investor bought asset S, S0=$100
 EOM Nov, asset target reached at $150 (sell)
 Sale yields gain of $50 (taxable)
 Wash-Sale Rule prohibits:
 Sell winner at $50 gain
 Sell another asset, Z that’s down $50 to $50 to
offset gain
 Buy asset Z back next day as investor still likes it
 Prohibited since trade is intentionally washing gain
1.19
Real World Situation - Tax


Alternative Synthetic using Options
Call Option (Strike = S0)
 Long has right to buy underlying at pre-specified price, S0
 Short has obligation to deliver underlying at that price
 Expiration Payoff Chart
+
+
S
-
S0
For the LONG
S0
S
-
For the SHORT
1.20
Real World Situation - Tax

Put Option (Struck at S0)
 Long has right to sell underlying at pre-specified price, S0
 Short has obligation to accept delivery of underlying at S0
 Expiration Payoff Chart
+
+
S0
S
S
-
S0
For the LONG
For the SHORT
1.21
Real World Situation - Tax

Consider the Synthetic (to offset 50 gain)
 Buy another Z asset at 50 in Nov (11/26/02)
 Sell an at-the-money call on Z
 Strike, Z0 = 50
 Expiration >= 31 days later, but in 2002 (12/30/02)
 Buy an at-the-money put on Z (same expiry)

At expiration, sell the Z asset or deliver
into Call
1.22
Real World Situation - Tax

Payoff Charts for the Synthetic
+
Price at the expiration of the options, Ze
50
Short
Call
Z
If Ze > 50:
•Short Call looses money
as short has to deliver Z for 50
•Long Put is worthless
Z
If Ze < 50:
•Short Call is worthless
•Long Put gains as the long can
sell Z for 50
Z
In either case the investor has
locked in the 50 price for the stock
1.23
bought at 100 (FIFO)
+
50
Long
Put
+
Synthetic
Short in Z
-
50
Real World Situation - Tax

The timing issue is important
 According to US Tax law, wash sale rules apply
if the investor acquires or sells a substantially
identical property within a 31-day period
 In the synthetic strategy, the second Z is
purchased on 11/20; while the options expire
on 12/30 when the first Z is sold (and the tax
loss is “booked” – FIFO accounting)
1.24
Real World Examples –
Consequences & Implications



Strategies are Risk Free and Zero Cost
(aside from commissions and fees)
We created a Synthetic (using Derivatives)
and used it to provide a solution
Finally, and most important, these examples
display the crucial role Legal & Regulatory
frameworks can play in engineering a
financial strategy (its the environment)
1.25
Two Points of View


Manufacturer (Dealer) vs. User (Investor)
Dealer’s View: there are two prices
 A price he will buy from you (low)
 A price he will sell to you (high)
 It’s how the dealer makes money

Dealer never has money; not like an investor
 Must find funding for any purchase
 Place the cash from any sale
 Leverage
1.26
Two Points of View

Dealers prefer to work with instruments
that have zero value at initiation (x bid/ask)
 Likely more liquid
 No principal risk

Regulators, Professional Organizations,
and the Law are more important for market
professionals than investors
 Dealers vs. Investors
1.27
The Nature of Derivatives
A derivative is an instrument whose value
depends on the values of other more
basic underlying variables
1.28
Examples of Derivatives
• Futures Contracts
• Forward Contracts
• Swaps
• Options
1.29
Derivatives Markets

Exchange traded
 Traditionally exchanges have used the openoutcry system, but increasingly they are switching
to electronic trading
 Contracts are standard; virtually no credit risk

Over-the-counter (OTC)
 A computer- and telephone-linked network of
dealers at financial institutions, corporations, and
fund managers
 Contracts can be non-standard and there is some
(small) amount of credit risk
1.30
Size of OTC and Exchange Markets
Source: Bank for International Settlements. Chart shows total principal amounts
for OTC market and value of underlying assets for exchange market
1.31
Ways Derivatives are Used





To hedge risks
To speculate (take a view on the future
direction of the market)
To lock in an arbitrage profit
To change the nature of a liability
To change the nature of an investment
without incurring the costs of selling one
portfolio and buying another
1.32
Forward Price


The forward price (for a contract) is the
delivery price that would be applicable
to a forward contract if were negotiated
today (i.e., the delivery price that would
make the contract worth exactly zero)
The forward price may be different for
contracts of different maturities
1.33
Terminology


The party that has agreed to buy
has what is termed a long position
The party that has agreed to sell
has what is termed a short position
1.34
Example



On May 24, 2010 the treasurer of a
corporation enters into a long forward
contract to buy £1 million in six months at
an exchange rate of 1.4422
This obligates the corporation to pay
$1,442,200 for £1 million on November 24,
2010
What are the possible outcomes?
1.35
Profit (or Payoff) from a
Long Forward Position
Profit
K
Price of Underlying
at Maturity, ST
Payoff at T = ST – K
1.36
Profit from a
Short Forward Position
Profit = Payoff at T = K - ST
K
Price of Underlying
at Maturity, ST
1.37
Foreign Exchange Quotes for GBP
May 24, 2010
Spot
Bid
1.4407
Offer
1.4411
1-month forward
1.4408
1.4413
3-month forward
1.4410
1.4415
6-month forward
1.4416
1.4422
1.38
Foreign Exchange Quotes for JPY
Jan 22, 2007 (16:23 EST)
Spot
Bid
121.62
Offer
121.63
1-month forward
121.08
121.09
3-month forward
120.17
120.18
6-month forward
118.75
118.77
1.39
1. Gold: An Arbitrage
Opportunity?
Suppose that:
• The spot price of gold is US$900
• The 1-year forward price of gold is
US$1,020
• The 1-year US$ interest rate is 5%
per annum
Is there an arbitrage opportunity?
1.40
2. Gold: Another Arbitrage
Opportunity?
Suppose that:
• The spot price of gold is US$900
• The 1-year forward price of gold is
US$900
• The 1-year US$ interest rate is 5%
per annum
Is there an arbitrage opportunity?
1.41
The Forward Price of Gold – The
Principal of Cash and Carry


If the spot price of gold is S(t0) and the forward price for
a contract deliverable in T years is F(t0,T), then
Can borrow money, buy gold, and sell the commodity
forward - where there should be no arbitrage:
F(t0,T) - S(t0) x (1+r )T = 0


where r is the 1-year money rate of interest to finance
the gold carry trade.
In our examples, S = 900, T = 1, and r =0.05 so that
F(t0,T) = 900(1+0.05) = 945
The no arbitrage 1 year forward price of gold is $945
1.42
The Forward Price of Gold – The
Principal of Cash and Carry

How does this come about?
S(t0)
receive
Borrow S(t0)
pay
S(t0)x(1+r)
t0
+
Gold
Buy Gold at S(t0)
S(t0)
+
F(t0)
Sell Gold Forward at F(t0)
Gold
=
Own
Deliver
No Arbitrage condition says:
Gold
Gold
F(t0) – S(t0)x(1+r) = 0
1.43
Gold Arbitrage?

The no arbitrage gold, 1-year forward condition is
F(t0,T) - S(t0) x (1+r )T = 0

If 1-year forward is $1020, then
F(t0,T) - S(t0) x (1+r )T > 0

so our strategy is to borrow money, buy gold, sell it forward, deliver
gold, and pay off loan for a riskless profit of $75
If 1-year forward is $900, then
F(t0,T) - S(t0) x (1+r )T < 0
and if I own gold, I can sell it, deposit proceeds, buy forward, pay
with the proceeds of the deposit and collect a riskless profit of $45
over the 1-year period
1.44
Futures Contracts



Agreement to buy or sell an asset for a
certain price at a certain time
Similar to forward contract
Whereas a forward contract is traded OTC,
a futures contract is traded on an
exchange
1.45
Futures Contracts


Forward contracts are similar to futures
except that they trade in the over-thecounter market
Forward contracts are particularly popular
on currencies and interest rates
1.46
Exchanges Trading Futures







Chicago Board of Trade (CME)
Chicago Mercantile Exchange
LIFFE (London)
Eurex (Europe)
BM&F (Sao Paulo, Brazil)
TIFFE (Tokyo)
and many more (see list at end of book)
1.47
Examples of Futures Contracts
Agreement to:
 Buy 100 oz. of gold @ US$1080/oz. in
December (NYMEX)
 Sell £62,500 @ 1.4410 US$/£ in
March (CME)
 Sell 1,000 bbl. of oil @ US$120/bbl. in
April (NYMEX)
1.48
Options
A call option is an option to buy a
certain asset by a certain date for a
certain price (the strike price)
 A put option is an option to sell a
certain asset by a certain date for a
certain price (the strike price)

1.49
American vs European Options


An American style option can be exercised
at any time during its life
A European style option can be exercised
only at maturity
1.50
Intel Option Prices (Sept 12, 2006;
Stock Price=19.56)
Strike
Price
Oct
Call
Jan
Call
Apr
Call
Oct
Put
Jan
Put
Apr
Put
15.00
4.650
4.950
5.150
0.025
0.150
0.275
17.50
2.300
2.775
3.150
0.125
0.475
0.725
20.00
0.575
1.175
1.650
0.875
1.375
1.700
22.50
0.075
0.375
0.725
2.950
3.100
3.300
25.00
0.025
0.125
0.275
5.450
5.450
5.450
1.51
Exchanges Trading Options







Chicago Board Options Exchange
American Stock Exchange
Philadelphia Stock Exchange
Pacific Exchange
LIFFE (London)
Eurex (Europe)
and many more (see list at end of book)
1.52
Options vs Futures/Forwards


A futures/forward contract gives the holder
the obligation to buy or sell at a certain
price
An option gives the holder the right to buy
or sell at a certain price
1.53
Types of Traders
• Hedgers
• Speculators
• Arbitrageurs
Some of the largest trading losses in derivatives have
occurred because individuals who had a mandate to be
hedgers or arbitrageurs switched to being speculators
(See, for example, SocGen (Jerome Kerviel) in Business
Snapshot 1.3, page 17)
1.54
Hedging Examples (pages 10-12)


A US company will pay £10 million for
imports from Britain in 3 months and
decides to hedge using a long position
in a forward contract
An investor owns 1,000 Microsoft
shares currently worth $28 per share. A
two-month put option with a strike price
of $27.50 costs $1. The investor
decides to hedge by buying 10
contracts
1.55
Hedging Example


A US company will pay £10 million for imports from
Britain in 3 months and decides to hedge using a
long position in a forward contract
Possible strategies:
 Buy £ now, deposit in bank, withdraw £10 million in 3 months,
pay for imports
 Buy £10 million forward in 3 months, deposit USD, use deposit
proceeds to settle and pay for imports
 Do nothing now and buy £10 million in the spot FX market in 3
months


First 2 are riskless, third has currency risk.
Which makes most sense?
1.56
Value of Microsoft Shares with
and without Hedging
40,000
Value of
Holding ($)
35,000
No Hedging
30,000
Hedging
25,000
Stock Price ($)
20,000
20
25
30
35
40
1.57
Speculation Example




An investor with $2,000 to invest feels
that a stock price will increase over the
next 2 months. The current stock price
is $20 and the price of a 2-month call
option with a strike of 22.50 is $1
What are the alternative strategies?
Buy 100 shares or
Buy 20 Calls (on 100 shares each)
1.58
Arbitrage Example




A stock price is quoted as £100 in
London and $140 in New York
The current exchange rate is 1.4410
What is the arbitrage opportunity?
Buy 100 shares in NY; sell 100 in
London
 = 100 [(1.441 x 100) – 140] = 410
1.59
Futures Contracts



Available on a wide range of underlyings
Exchange traded
Specifications need to be defined:
 What can be delivered,
 Where it can be delivered, &
 When it can be delivered

Settled daily
1.60
Forward Contracts vs Futures
Contracts
FORWARDS
FUTURES
Private contract between 2 parties
Exchange traded
Non-standard contract
Standard contract
Usually 1 specified delivery date
Settled at end of contract
Delivery or final cash
settlement usually occurs
Some credit risk
Range of delivery dates
Settled daily
Contract usually closed out
prior to maturity
Virtually no credit risk
1.61
Margins

A margin is cash or marketable securities
deposited by an investor with the broker
 Initial Margin
 Maintenance Margin


The balance in the margin account is
adjusted to reflect daily settlement
Margins minimize the possibility of a loss
through a default on a contract
1.62
Example: Futures Trade (page 27-28)
1.63
A Possible Outcome
Table 2.1, Page 28
1.64
Other Key Points About Futures



They are settled daily
Closing out a futures position
involves entering into an offsetting
trade
Most contracts are closed out
before maturity
1.65
Collateralization in OTC Markets


It is becoming increasingly common for
contracts to be collateralized in OTC
markets
They are then similar to futures contracts
in that they are settled regularly (e.g. every
day or every week)
1.66
Another Detail for Cash and
Carry Arbitrage

Contract price changes with longer term
 Higher or Lower


To this point we have neglected storage cost
Lets re-visit no-arbitrage equation
F(t0,T) - S(t0) x [(1+r )T ] = Storage (T)



Storage costs ignored in earlier gold example
No storage costs for FX
Convenience Yield
1.67
1. Oil: An Arbitrage Opportunity?
Suppose that:
- The spot price of oil is US$95
- The quoted 1-year futures price of
oil is US$125
- The 1-year US$ interest rate is
5% per annum
- The storage costs of oil are 2% per
annum
Is there an arbitrage opportunity?
1.68
2. Oil: Another Arbitrage
Opportunity?
Suppose that:
- The spot price of oil is US$95
- The quoted 1-year futures price of
oil is US$80
- The 1-year US$ interest rate is
5% per annum
- The storage costs of oil are 2%
per annum
Is there an arbitrage opportunity?
1.69
Futures Prices for Gold on Jan 8, 2007: Prices
Increase with Maturity
Futures Price ($ per oz)
650
640
630
620
610
Contract Maturity Month
600
Jan-07
Apr-07
Jul-07
Oct-07
Jan-08
1.70
Futures Price (cents per lb)
Futures Prices for Orange Juice on Jan 8, 2007:
Prices Decrease with Maturity
210
205
200
195
190
185
180
175
170
Jan-07
Contract Maturity Month
Mar-07
May-07
Jul-07
Sep-07
Nov-07
1.71
Delivery


If a futures contract is not closed out before
maturity, it is usually settled by delivering the
assets underlying the contract. When there are
alternatives about what is delivered, where it is
delivered, and when it is delivered, the party with
the short position chooses.
A few contracts (for example, those on stock
indices and Eurodollars) are settled in cash
1.72
Some Terminology



Open interest: the total number of contracts
outstanding
 equal to number of long positions or
number of short positions
Settlement price: the price just before the
final bell each day
 used for the daily settlement process
Volume of trading: the number of contracts
traded in 1 day
1.73
Convergence of Futures to Spot
Futures
Price
Spot Price
Futures
Price
Spot Price
Time
(a)
Time
(b)
1.74
Questions


When a new trade is completed what
are the possible effects on the open
interest?
Can the volume of trading in a day
be greater than the open interest?
1.75
Regulation of Futures

Regulation is designed to protect
the public interest
 CFTC – the Feds

Regulators try to prevent
questionable trading practices by
either individuals on the floor of
the exchange or outside groups
 NFA – the industry
1.76
The End for Today

Questions?
1.77