1. FE-W http://pluto.mscc.huji.ac.il/~mswiener/zvi.html EMBAF Zvi Wiener mswiener@mscc.huji.ac.il 02-588-3049 Financial Engineering

2. FE-W http://pluto.mscc.huji.ac.il/~mswiener/zvi.html EMBAF Following Paul Wilmott, Introduces Quantitative Finance Chapter 12 An Introduction to Exotic And Path-Dependent Options

3. Zvi WienerFE-Wilmott-IntroQF Ch12 slide 3 Early Exercise Bermudian options American options

4. Zvi WienerFE-Wilmott-IntroQF Ch12 slide 4 Weak Path Dependence Barrier knock-in, knock-out, multiple touch Example: As long as an underlying remains below 150 during the life of a contract, the payoff will be call at maturity, otherwise nothing!

5. Zvi WienerFE-Wilmott-IntroQF Ch12 slide 5 Black-Scholes-Merton Equation time S T ? 0 payoff barrier

6. Zvi WienerFE-Wilmott-IntroQF Ch12 slide 6 Strong Path Dependence Asian options Accrual notes Strike = mean, Minimum, Maximum, etc. Typically increases dimensionality of the problem.

7. Zvi WienerFE-Wilmott-IntroQF Ch12 slide 7 Compounds and Choosers options on options. The compound option gives the holder the right to buy (sell) another option The chooser option gives the right to buy another option at his choice. Extendible options allow to change expiration and strike.

8. Zvi WienerFE-Wilmott-IntroQF Ch12 slide 8 Black-Scholes-Merton Equation time S T ? 0 Payoff = another option, or Max(Put, Call)

9. Zvi WienerFE-Wilmott-IntroQF Ch12 slide 9 Range Notes Pays at rate Ldt all the time when the underlying lies within a range S d <S<S u Denote I(S)=1 when S is in the range, and 0 otherwise.

10. Zvi WienerFE-Wilmott-IntroQF Ch12 slide 10 Range time S T ? Ldt 00

11. Zvi WienerFE-Wilmott-IntroQF Ch12 slide 11 Lookback Options The payoff depends on the Maximal, Minimal value of the underlying asset during some period of time.

12. Zvi WienerFE-Wilmott-IntroQF Ch12 slide 12 Home Assignment Read chapter 12 in Wilmott.