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  [email protected]

 Office: WH 212A; 410-516-7136  Office Hours: 4:30 – 5:30 Monday  Teaching Assistant(s)  Huang, Qiushun ( [email protected]

)  Office Hours: Friday 4pm – 6pm  Ward, Brian ( [email protected]

)  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 Investment Banking New Issue Securities Make Markets Broker-Dealers & Exchanges Securities & Contracts Manage Invested Funds Institutional Investors

1.13

Two Fundamental Ideas in Modeling

LOAN FROM STANDPOINT OF LENDER

 Cash Flow  Cash flow diagram  Receive vs. Pay over Time

Receive Pay

Repayment of Loan w/Interest at t 0 +T t, time Amount of Loan, t 0  Payoff Cashflow

Gain

 Payoff diagram  Gain vs. Loss against Price  Cashflows can depend

Loss

on some other variable S, Price K

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) USD T = 1/4 year Lt 0 = 3 month interest rate in effect at t 0 t 0 + T t 0

Borrow: USD Pay Back: USD

x

(1

+

Lt 0

x

T)

Pay Back USD+Lt 0 x(.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(t 0 ,Y)  Sell Yen and buy USD in spot FX mkt at e(t 0 ,Y)  Finally, the bank buys Yen and sells USD in the forward FX market for delivery at t 0 +T

1.16

Real World Situation - Cash

 Cash Flows are Additive Y t 0 USD + Y USD + =

Borrow Y for T

Yx(1+L(t 0 ,Y)xT)

Buy USD sell Y at e(t 0 ,Y)

Y = e(t 0 ,Y) x USD Yx(1+L(t 0 ,Y)xT) USDx(1+L(t 0 ,$)xT)

Buy Y forward for t 0 +T

Y x (1 + L(t 0 ,Y)xT) = f(t 0 ,T;Y) x USD1 USD1 = USD x (1 + L(t 0 ,$) x T) t 0 +T USDx(1+L(t 0 ,$)xT)

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, ex credit 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, S 0 =$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

= S 0 ) Long has right to buy underlying at pre-specified price, S 0  Short has obligation to deliver underlying at that price 

Expiration

Payoff Chart + + S 0 S S S 0 For the LONG For the SHORT

1.20

Real World Situation - Tax

 Put Option (Struck at S 0 )  Long has right to sell underlying at pre-specified price, S 0  Short has obligation to accept delivery of underlying at S 0  Expiration Payoff Chart + S 0 S + S 0 S 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, Z 0 = 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, Z e 50

Short Call

+ Z If Z e > 50: •Short Call looses money as short has to deliver Z for 50 •Long Put is worthless 50

Long Put

+ Z If Z e < 50: •Short Call is worthless •Long Put gains as the long can sell Z for 50 50

Synthetic Short in Z

Z In either case the investor has locked in the 50 price

for the stock bought at 100 (FIFO) 1.23

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 open outcry 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,

S T

Payoff at

T

=

S T – K

1.36

Profit from a Short Forward Position

Profit = Payoff at

T

=

K - S T K

Price of Underlying at Maturity,

S T

1.37

Foreign Exchange Quotes for GBP May 24, 2010

Spot 1-month forward 3-month forward 6-month forward Bid 1.4407

1.4408

1.4410

1.4416

Offer 1.4411

1.4413

1.4415

1.4422

1.38

Foreign Exchange Quotes for JPY Jan 22, 2007 (16:23 EST)

Spot Bid 121.62

1-month forward 121.08

3-month forward 120.17

6-month forward 118.75

Offer 121.63

121.09

120.18

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(t 0 )

a contract deliverable in

T

and the forward price for years is

F(t 0 ,T)

, then Can borrow money, buy gold, and sell the commodity forward -

where there should be no arbitrage: F(t 0 ,T) - S(t 0 )

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(t 0 ,T)

The

no arbitrage

= 900(1+0.05) = 945 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) S(t0)x(1+r)

pay t0

+ Gold Buy Gold at S(t0) S(t0) + F(t0) Sell Gold Forward at F(t0) Gold = No Arbitrage condition says:

Own

Gold

Deliver

Gold F(t0) – S(t0)x(1+r) = 0 1.43

Gold Arbitrage?

   The no arbitrage gold, 1-year forward condition is

F(t 0 ,T) - S(t 0 )

x If 1-year forward is $1020, then (1+

r

)

T = 0 F(t 0 ,T) - S(t 0 )

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(t 0 ,T) - S(t 0 )

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-the counter 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 15.00

Oct Call 4.650

Jan Call 4.950

Apr Call 5.150

Oct Put 0.025

Jan Put 0.150

Apr Put 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 30,000 25,000 20,000 20 25 30

Stock Price ($)

35 40 No Hedging Hedging

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

Private contract between 2 parties Non-standard contract Usually 1 specified delivery date Settled at end of contract Delivery or final cash settlement usually occurs Some credit risk

FUTURES

Exchange traded Standard contract 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

650 640 630 620 610 600 Jan-07 Apr-07 Jul-07

Contract Maturity Month

Oct-07 Jan-08

1.70

Futures Prices for Orange Juice on Jan 8, 2007: Prices Decrease with Maturity

210 205 200 195 190 185 180 175 170 Jan-07 Mar-07 May-07 Jul-07

Contract Maturity Month

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

Spot Price Futures Price Time (a) Futures Price Spot Price 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