FE-Whttp://pluto.mscc.huji.ac.il/

~mswiener/zvi.htmlEMBAF

Zvi Wiener

mswiener@mscc.huji.ac.il

02-588-3049

Financial Engineering

Zvi Wiener FE-Wilmott-Ch1-2 slide 2

Financial Engineering

Zvi Wiener

Head of Finance Department

The Hebrew University of Jerusalem

02-588-3049, mswiener@mscc.huji.ac.il

Alon Raviv

???

rmidbary@ovedgubi.com

Zvi Wiener FE-Wilmott-Ch1-2 slide 3

Textbook

Paul Wilmott Introduces Quantitative Finance

John Wiley and Sons, 2001

See also

http://www.wilmott.com

http://www.paulwilmott.com

Zvi Wiener FE-Wilmott-Ch1-2 slide 4

Money Market Account

dttMtrtMdttM )()()()(

dttMtrtMdttM )()()()(

)()( tMtrdt

dM

t

dtr

eMtM 0

)(

)0()(

Zvi Wiener FE-Wilmott-Ch1-2 slide 5

Forward contract (1.9.1)Asset is traded at $S0 (spot price).

What is the forward price at time T?

We can take a loan, buy the asset for $S0 and

wait till T.

Or we can enter a forward contract maturing at T with a forward price F.

Zvi Wiener FE-Wilmott-Ch1-2 slide 6

Forward contract (1.9.1)Forward contract:

Today (0) sign a forward contract with forward price F.

At time T pay F, get ST.

Time 0 TMoney 0 ST-F

Zvi Wiener FE-Wilmott-Ch1-2 slide 7

Forward contract (1.9.1)Take a loan for $S0,

buy the stock today,

wait till T,

return the loan

0 T-S0 ST

+S0 -S0erT

Zvi Wiener FE-Wilmott-Ch1-2 slide 8

Forward contract (1.9.1)

The forward price (if no carry) should be

FT = S0 erT

If there are storage costs and convenience yield the formula becomes

TcsrT eSF )(

0

FE-Whttp://pluto.mscc.huji.ac.il/

~mswiener/zvi.htmlEMBAF

Following

Paul Wilmott, Introduces Quantitative Finance

Chapter 2

Derivatives

Zvi Wiener FE-Wilmott-Ch1-2 slide 10

Derivatives and Risk Management

Stocks and bonds are securities – issued to raise capital.

Derivatives are contracts, agreements used for risk transfer.

Zvi Wiener FE-Wilmott-Ch1-2 slide 11

Financial Derivatives

Futures, Forwards, Swaps

Options

European, American, Asian, Parisian

Call, Put

Cap, Floor

Credit derivatives

Zvi Wiener FE-Wilmott-Ch1-2 slide 12

Types of Financial Risks

Market Risk

Credit Risk

Liquidity Risk

Operational Risk

Legal Risk

Zvi Wiener FE-Wilmott-Ch1-2 slide 13

Call Option

The right to buy a particular asset for an agreed amount at a specified time in the future.

Payoff = Max(S-E, 0)

Notional

Strike

Maturity

Underlying

Volatility

Zvi Wiener FE-Wilmott-Ch1-2 slide 14

Put Option

The right to sell a particular asset for an agreed amount at a specified time in the future.

Payoff = Max(E-S, 0)

Time value

Intrinsic value

At-the-Money

In-the-money

Out-of-the-money

Zvi Wiener FE-Wilmott-Ch1-2 slide 15

Common terms

Long and Short positions

Margin

Early exercise

Put-Call parity

Zvi Wiener FE-Wilmott-Ch1-2 slide 16

Value of an Option at Expiration

E. Call

X Underlying

Zvi Wiener FE-Wilmott-Ch1-2 slide 17

Call Value before Expiration

E. Call

X Underlying

Zvi Wiener FE-Wilmott-Ch1-2 slide 18

Call Value before Expiration

E. Call

X Underlying

premium

Zvi Wiener FE-Wilmott-Ch1-2 slide 19

Put Value at Expiration

E. Put

X Underlying

X

Zvi Wiener FE-Wilmott-Ch1-2 slide 20

Put Value before Expiration

E. Put

X Underlying

premium

X

Zvi Wiener FE-Wilmott-Ch1-2 slide 21

Speculation

S=$666

Call with strike 680 and 4M to maturity is $39

If you expect the stock price to raise

Buy the stock for 666, sell it for 730

Have (730-666)/666 = 9.6% profit in 4M

If you buy the option you get

(730-666-39)/39 = 28% on ($39)

Zvi Wiener FE-Wilmott-Ch1-2 slide 22

Binary (Digital) Call option

K S

Zvi Wiener FE-Wilmott-Ch1-2 slide 23

Binary (Digital) Put option

K S

Zvi Wiener FE-Wilmott-Ch1-2 slide 24

Bull Spread

K S

Zvi Wiener FE-Wilmott-Ch1-2 slide 25

Bear Spread

K S

Zvi Wiener FE-Wilmott-Ch1-2 slide 26

Straddle option

K S

Zvi Wiener FE-Wilmott-Ch1-2 slide 27

Strangle option

S

Zvi Wiener FE-Wilmott-Ch1-2 slide 28

Buttrefly

S

Zvi Wiener FE-Wilmott-Ch1-2 slide 29

Condor

S

Zvi Wiener FE-Wilmott-Ch1-2 slide 30

Warrants

Dilution effect

Endowment warrants

Perpetual warrants

Convertible bonds

Zvi Wiener FE-Wilmott-Ch1-2 slide 31

Collar

Firm B has shares of firm C of value $200M

They do not want to sell the shares, but need

money.

Moreover they would like to decrease the

exposure to financial risk.

How to get it done?

Zvi Wiener FE-Wilmott-Ch1-2 slide 32

Collar

1. Buy a protective Put option (3y to maturity,

strike = 90% of spot).

2. Sell an out-the-money Call option (3y to

maturity, strike above spot).

3. Take a “cheap” loan at 90% of the current

value.

Zvi Wiener FE-Wilmott-Ch1-2 slide 33

Collar payoff

payoff

90 100 K stock

90

K

Zvi Wiener FE-Wilmott-Ch1-2 slide 34

Options in Hi Tech

Many firms give options as a part of

compensation.

There is a vesting period and then there is a

longer time to expiration.

Most employees exercise the options at

vesting with same-day-sale (because of tax).

How this can be improved?

Zvi Wiener FE-Wilmott-Ch1-2 slide 35

Long term options

payoff

k K stock

50

K

Sell a call

Your option

Result

Zvi Wiener FE-Wilmott-Ch1-2 slide 36

ExampleYou have 10,000 vested options for 10 years

with strike $5, while the stock is traded at $10.

An immediate exercise will give you $50,000

before tax.

Selling a (covered) call with strike $15 will

give you $60,000 now (assuming interest rate

6% and 50% volatility) and additional profit at

the end of the period!

Zvi Wiener FE-Wilmott-Ch1-2 slide 37

Example

payoff

10 15 26

50

K

Your option

Result

60

exercise

Zvi Wiener FE-Wilmott-Ch1-2 slide 38

Home assignment

Read chapters 1-2.

Visit

www.liffe.com

www.nyse.com

www.cboe.com