EMBAF

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Financial Engineering

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

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The Black-Scholes model

• Following
• Paul Wilmott, Introduces Quantitative Finance
• Chapter 8

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Notations

• V(S, t ?, ? E, T r)
• S and t are variables
• ? and ? are parameters of the asset
• E and T are parameters of the contract
• r is parameter of the currency

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Assumption

• Perfect markets
• Complete markets
• No arbitrage.
• Risk factor dynamics

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Assumptions of BS

• The underlying price moves continuously
• Interest rates are known and constant
• The variance of returns is constant
• Perfect capital markets
• no transaction costs
• short sales are allowed
• markets operate continuously
• price taking

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V(S,t)
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Delta Hedging

• Form a delta-balanced portfolio V-?S

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No Arbitrage
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Black-Scholes-Merton Equation
S
?
payoff
time
T
0
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Black-Scholes-Merton Equation

• Read at home
• Dividend-paying stock
• Currency
• Commodity
• Forwards
• Options on Futures

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(No Transcript)
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DigitalBinary options

• Payoff 1 if STgtK, and 0 otherwise (Call)

Payoff at maturity
stock
K
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DigitalBinary options

• Payoff 1 if STltK, and 0 otherwise (Put)

Payoff at maturity
stock
K
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Exchange Option (Margrabe 78)

• r should be replaced by the difference of yields
  of the two assets.

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Home Assignment

• Read chapter 8 in Wilmott.
• Follow Excel files coming with the book.