1.1

550.444Introduction to

Financial Derivatives

IntroductionWeeks of September 4 and

September 9, 2013

1.2

Principals David R Audley, Ph.D.; Sr. Lecturer in AMS

david.audley@jhu.eduOffice: WH 212A; 410-516-7136Office Hours: 4:30 – 5:30 Monday

Teaching Assistant(s)Huang, Qiushun (qhuang13@jhu.edu)

Office Hours: Friday 4pm – 6pmWard, Brian (bward16@jhu.edu)

Office Hours: Monday & Wednesday 2pm – 3 pm

1.3

Schedule Lecture Encounters

Monday & Wednesday, 3:00 - 4:15pm,Mergenthaler 111

SectionSection 1: Friday 3:00 - 3:50pm, Hodson 211Section 2: Thursday 3:00 - 3:50pm, WH 304

1.4

Protocol Attendance

Lecture – Mandatory (default) for MSE Fin Math majorsQuizzes & 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

1.5

Resources Textbook

John C Hull: Options, Futures, and Other Derivatives, Prentice-Hall 2012 (8e)Recommended: Student Solutions Manual

On Reserve in LibraryText Resources

http://www.rotman.utoronto.ca/~hull/ofod/Errata8e/index.htmlhttp://www.rotman.utoronto.ca/~hull/TechnicalNotes/index.html

1.6

Resources Supplemental Material

As directed AMS Website

http://jesse.ams.jhu.edu/~daudley/444Additional Subject Material

Class Resources & Lecture SlidesIndustry & Street “Research” (Optional)

Consult at your leisure/riskInterest can generate Special Topics sessions

Blackboard

1.7

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)

1.8

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

1.9

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

1.10

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)

1.11

How Things Work True Assets – A house, a company, oil, … Ownership rights, contracts, & other legal

instruments which represent the true assetFor us, many are indistinguishable from the

asset; are the assetProvide properties that can be quantified,

assigned, subordinated and made contingentCan be modeled

1.12

Who Makes it Work Investment Banks: Capital Intermediation

Companies into StockBorrowings into Bonds

Broker-Dealers & Markets (Exchanges)Create everything elseFacilitate transfer/exchange (trading)

Investors Under the Watchful Eyes of Regulators,

Professional Associations and the Rule of Law

1.13

Creation & Exchange of Securities and Instruments

Create Securities

Make Markets

Manage Invested Funds

Collateral

New Issue Securities

Securities & Contracts

Secondary Issues

Investment Banking Broker-Dealers &Exchanges

Institutional Investors

1.14

Two Fundamental Ideas in Modeling Cash Flow

Cash flow diagramReceive vs. Pay over Time

Payoff CashflowPayoff diagram

Gain vs. Loss against PriceCashflows can depend on some other variable

Receive

Pay

LOAN FROM STANDPOINT OF LENDER

Amount of Loan, t0

Repayment of Loan w/Interest at t0+T

t, time

Gain

Loss

S, PriceK

LONG STOCK ATPRICE K

1.15

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

t0

t0 + T

USD

USD+Lt0x(.25)xUSD

T = 1/4 yearLt0 = 3 month interest rate in effect at t0

Borrow: USDPay Back: USD x (1 + Lt0 x T)

Receive(Borrow)

Pay Back

1.16

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 mktBorrow 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

1.17

Real World Situation - Cash Cash Flows are Additive

+

+

=

t0 t0+T

Y

Yx(1+L(t0,Y)xT)USD

Y Yx(1+L(t0,Y)xT)

USD

USDx(1+L(t0,$)xT)

Borrow Y for T

Buy USD sell Y at e(t0,Y)

Y = e(t0,Y) x 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)

1.18

Real World Situation - Cash What’s the difference; what’s interesting

International Banks have credit risk in the USD loanFor the synthetic, the International Bank exposure is in

the forward contract onlyNo principal riskYen 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 hedgeDifferent markets involve many legal & regulatory

differences

1.19

Real World Situation - Tax Situation:

In Sept ‘02, investor bought asset S, S0=$100EOM Nov, asset target reached at $150 (sell)Sale yields gain of $50 (taxable)Wash-Sale Rule prohibits:

Sell winner at $50 gainSell another asset, Z that’s down $50 to $50 to

offset gainBuy asset Z back next day as investor still likes itProhibited since trade is intentionally washing gain

1.20

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 priceExpiration Payoff Chart

+

-

+

-S0

SS0

S

For the LONG For the SHORT

1.21

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

+

-

S

+

-

SS0

S0

For the LONG For the SHORT

1.22

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 = 50Expiration >= 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

1.23

Real World Situation - Tax Payoff Charts for the Synthetic

50+

-

Z

50+

-

Z

50+

-

Z

ShortCall

LongPut

SyntheticShort in Z

Price at the expiration of the options, Ze

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

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

In either case the investor haslocked in the 50 price for the stockbought at 100 (FIFO)

1.24

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)

1.25

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)

1.26

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 investorMust find funding for any purchasePlace the cash from any saleLeverage

1.27

Two Points of View Dealers prefer to work with instruments

that have zero value at initiation (x bid/ask)Likely more liquidNo principal risk

Regulators, Professional Organizations, and the Law are more important for market professionals than investors

Dealers vs. Investors

1.28

The Nature of Derivatives

A derivative is an instrument whose value depends on the values of other more basic underlying variables

1.29

Examples of Derivatives

• Futures Contracts• Forward Contracts• Swaps• Options

1.30

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

1.31

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

1.32

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

1.33

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

1.34

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

1.35

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?

1.36

Profit (or Payoff) from aLong Forward Position

Profit

Price of Underlying at Maturity, STK

Payoff at T = ST – K

1.37

Profit from a Short Forward Position

Profit = Payoff at T = K - ST

Price of Underlying at Maturity, STK

1.38

Foreign Exchange Quotes for GBP May 24, 2010

Bid OfferSpot 1.4407 1.4411

1-month forward 1.4408 1.4413

3-month forward 1.4410 1.4415

6-month forward 1.4416 1.4422

1.39

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

Bid OfferSpot 121.62 121.63

1-month forward 121.08 121.09

3-month forward 120.17 120.18

6-month forward 118.75 118.77

1.40

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 annumIs there an arbitrage opportunity?

1.41

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 annumIs there an arbitrage opportunity?

1.42

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 = 0where 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 thatF(t0,T) = 900(1+0.05) = 945

The no arbitrage 1 year forward price of gold is $945

1.43

The Forward Price of Gold – The Principal of Cash and Carry How does this come about?

S(t0)

t0

receive

pay S(t0)x(1+r)

Gold

S(t0)

F(t0)

Gold

Own

Deliver

Gold

Gold

Borrow S(t0)

Buy Gold at S(t0)

Sell Gold Forward at F(t0)

No Arbitrage condition says:

F(t0) – S(t0)x(1+r) = 0

+

+

=

1.44

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 > 0so 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 < 0and 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

1.45

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

1.46

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

1.47

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)

1.48

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)

1.49

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)

1.50

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

1.51

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

1.52

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)

1.53

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

1.54

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)

1.55

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

1.56

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?

1.57

Value of Microsoft Shares with and without Hedging

20,000

25,000

30,000

35,000

40,000

20 25 30 35 40

Stock Price ($)

Value of Holding ($)

No Hedging

Hedging

1.58

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)

1.59

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

1.60

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

1.61

Forward Contracts vs Futures Contracts

Private contract between 2 parties Exchange traded

Non-standard contract Standard contract

Usually 1 specified delivery date Range of delivery dates

Settled at end of contract Settled daily

Delivery or final cashsettlement usually occurs

Contract usually closed outprior to maturity

FORWARDS FUTURES

Some credit risk Virtually no credit risk

1.62

Margins A margin is cash or marketable securities

deposited by an investor with the brokerInitial MarginMaintenance 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

1.63

Example: Futures Trade (page 27-28)

1.64

A Possible OutcomeTable 2.1, Page 28

1.65

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

1.66

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)

1.67

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

1.68

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

annumIs there an arbitrage opportunity?

1.69

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 annumIs there an arbitrage opportunity?

1.70

Futures Prices for Gold on Jan 8, 2007: Prices Increase with Maturity

Jan-07 Apr-07 Jul-07 Oct-07 Jan-08600

610

620

630

640

650

Contract Maturity MonthFutu

res

Pric

e ($

per

oz)

1.71

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

Jan-07 Mar-07 May-07 Jul-07 Sep-07 Nov-07170

175

180

185

190

195

200

205

210

Contract Maturity Month

Futu

res

Pric

e (c

ents

per

lb)

1.72

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

1.73

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

1.74

Convergence of Futures to Spot

Time Time

(a) (b)

FuturesPrice

FuturesPrice

Spot Price

Spot Price

1.75

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?

1.76

Regulation of Futures

Regulation is designed to protect the public interestCFTC – the Feds

Regulators try to prevent questionable trading practices by either individuals on the floor of the exchange or outside groupsNFA – the industry

1.77

The End for Today Questions?