1 / 14

Chapter 4

Chapter 4. Financial Engineering --- Nesting GARCH and GARCH Option Pricing Theory. A. GARCH Family History. (A) ARCH(R.Engle,1982). ARCH(1):. (B) GARCH(T.Bollerslev,1986). GARCH(1,1). (C) GARCHM (Engle and Bollerslev,1986). GARCHM(1,1). (D) EGARCH (D. Nelson, 1991). EGARCH(1,1).

taya
Download Presentation

Chapter 4

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. Chapter 4 Financial Engineering --- Nesting GARCH and GARCH Option Pricing Theory

  2. A. GARCH Family History

  3. (A) ARCH(R.Engle,1982) ARCH(1):

  4. (B) GARCH(T.Bollerslev,1986) GARCH(1,1)

  5. (C) GARCHM (Engle and Bollerslev,1986) GARCHM(1,1)

  6. (D) EGARCH (D. Nelson, 1991) EGARCH(1,1)

  7. (E) NAGARCH (Engle and Ng, 1993) NAGARCH(1,1)

  8. B.GARCH Option Pricing

  9. (A)Assumptions 1.The spot price S(t) follow NAGARCH-M process • p=q=1 and β1+α1r12＜1 • Continuous-time limit

  10. Risk-neutral form where, 2.The value of a call option with one period to expiration obeys the Black-Sholes-Rubinstein formula.

  11. (B)Model • Proposition I: The risk-neutral process takes the same NAGARCH form with λ replaced by –1/2 and r1 replaced by r1*= r1+λ+1/2

  12. Proposition II: The generating function takes the log-linear form where for the single log(p=q=1) version and these coefficients can be calculated recursively from the terminal conditions: A(T;T,ψ)=0 B1(T;T,ψ)=0

  13. Proposition III: If the characteristic function of the log spot price is f(iψ), then where Re[ ] denotes the real part of a complex number.

  14. European call option: Et*[ ]: denotes the expectation under risk-neutral distribution.

More Related