EMBAF

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Financial Engineering

• Zvi Wiener
• mswiener_at_mscc.huji.ac.il
• 02-588-3049

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Financial Engineering

• Zvi Wiener
• Head of Finance Department
• The Hebrew University of Jerusalem
• 02-588-3049, mswiener_at_mscc.huji.ac.il

Alon Raviv ??? rmidbary_at_ovedgubi.com
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Textbook

• Paul Wilmott Introduces Quantitative Finance
• John Wiley and Sons, 2001
• See also
• http//www.wilmott.com
• http//www.paulwilmott.com

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Money Market Account
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.

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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 T Money 0 ST-F
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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
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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

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Derivatives

• Following
• Paul Wilmott, Introduces Quantitative Finance
• Chapter 2

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Derivatives and Risk Management

• Stocks and bonds are securities issued to raise
  capital.
• Derivatives are contracts, agreements used for
  risk transfer.

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Financial Derivatives

• Futures, Forwards, Swaps
• Options
• European, American, Asian, Parisian
• Call, Put
• Cap, Floor
• Credit derivatives

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Types of Financial Risks

• Market Risk
• Credit Risk
• Liquidity Risk
• Operational Risk
• Legal Risk

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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

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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

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Common terms

• Long and Short positions
• Margin
• Early exercise
• Put-Call parity

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Value of an Option at Expiration
E. Call
X Underlying
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Call Value before Expiration
E. Call
X Underlying
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Call Value before Expiration
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Put Value at Expiration
E. Put
X
X Underlying
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Put Value before Expiration
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Speculation

• S666
• 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)

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Binary (Digital) Call option
K S
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Binary (Digital) Put option
K S
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Bull Spread
K S
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Bear Spread
K S
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Straddle option
K S
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Strangle option
S
28
Buttrefly
S
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Condor
S
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Warrants

• Dilution effect
• Endowment warrants
• Perpetual warrants

Convertible bonds
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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?

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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.

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Collar payoff
payoff
K
90
90 100 K stock
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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?

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Long term options
payoff
K
50
k K stock
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Example

• You 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!

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Example
payoff
K
60
50
10 15 26
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Home assignment

• Read chapters 1-2.
• Visit
• www.liffe.com
• www.nyse.com
• www.cboe.com