1 / 12

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 .

carmeliaj
Download Presentation

Financial Engineering

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related