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Financial Engineering

Financial Engineering. Zvi Wiener mswiener@mscc.huji.ac.il 02-588-3049. Barrier Options. Following Paul Wilmott, Introduces Quantitative Finance Chapter 13. Types of Barrier Options. Out option pays off if a level is not reached, otherwise it is knocked out .

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Financial Engineering

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

  2. Barrier Options Following Paul Wilmott, Introduces Quantitative Finance Chapter 13 http://pluto.mscc.huji.ac.il/~mswiener/zvi.html

  3. Types of Barrier Options • Out option pays off if a level is not reached, otherwise it is knocked out. • In option pays as long as a level is reached (knocked in). • Payoff classification is standard: call, put, binary, etc. • Double barrier there are both up and down barriers. • Sometimes a rebate is paid if barrier is reached. FE-Wilmott-IntroQF Ch13

  4. R S PDE approach to barriers, Out S V=R (rebate) Out barrier ? Payoff T time V=0 FE-Wilmott-IntroQF Ch13

  5. PDE approach to barriers, In S Two stages: first a regular option above the barrier, this provides a boundary condition. Second the In option is solved with this boundary condition. Regular option In barrier ? Payoff T time V=0 FE-Wilmott-IntroQF Ch13

  6. Down-and-in call + Down-and-out call = Plain call option FE-Wilmott-IntroQF Ch13

  7. Up-and-out call option Value of an up-and-out call S barrier FE-Wilmott-IntroQF Ch13

  8. Other features • Early exercise, American or Bermudian style • Repeated hitting (both up and down) • Dynamic barrier • Rainbow: payoff determined by asset A, while barrier by asset B. • Soft barriers – (dis)appear gradually • Alon Raviv – default option as a soft barrier. FE-Wilmott-IntroQF Ch13

  9. Volatility • Most analytical models assume constant volatility. • In practice there is a smile/smirk effect. • It is very important to keep in mind vega as a risk factor! • Bid-ask in terms of vol. FE-Wilmott-IntroQF Ch13

  10. Hedging Barrier Options • Approximate hedge with other options, see 13.7 • Delta hedge is problematic at boundaries, since delta is not continuous there (slippage costs). • Solution – smoothing of delta hedging with minimization of tracking error. FE-Wilmott-IntroQF Ch13

  11. Analytic Formulas for Barriers • Up-and-out call/put • Up-and-in call/put • Down-and-out call/put • Down-and-in call/put • See formulas in section 13.8 FE-Wilmott-IntroQF Ch13

  12. Home Assignment • Read chapter 13 in Wilmott. • Classify all structured products that we have discussed as types of barriers (POALIM, LEUMI, etc.) • Plot the appropriate area for PDE and boundary conditions. FE-Wilmott-IntroQF Ch13

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