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Wiener Process and Ito's lemma process

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Ninoto Zhimomi
Ninoto Zhimomi

Ch12 Hull

FormationBusinessÉconomie & finance
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Wiener Processes and Itô’s Lemma Chapter 12 Options, Futures, and Other Derivatives, 7th Edition, Copyright © John C. Hull 2008
Types of Stochastic Processes ,[object Object],[object Object],[object Object],[object Object],Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008
Modeling Stock Prices ,[object Object],[object Object],Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008
Markov Processes (See pages 259-60) ,[object Object],[object Object],Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008
Weak-Form Market Efficiency ,[object Object],[object Object],Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008
Example of a Discrete Time Continuous Variable Model ,[object Object],[object Object],Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008
Questions ,[object Object],[object Object],[object Object],[object Object],[object Object],Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008
Variances & Standard Deviations ,[object Object],[object Object],[object Object],Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008
Variances & Standard Deviations (continued) ,[object Object],[object Object],Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008
A Wiener Process (See pages 261-63) ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008
Properties of a Wiener Process ,[object Object],[object Object],[object Object],Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008
Taking Limits . . . ,[object Object],[object Object],[object Object],Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008
Generalized Wiener Processes (See page 263-65) ,[object Object],[object Object],Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008
Generalized Wiener Processes (continued) ,[object Object],[object Object],Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008
Generalized Wiener Processes (continued) ,[object Object],[object Object],[object Object],Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008
The Example Revisited ,[object Object],[object Object],[object Object],[object Object],[object Object],Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008
It ô Process (See pages 265) ,[object Object],[object Object],[object Object],[object Object],[object Object],Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008
Why a Generalized Wiener Process Is Not Appropriate for Stocks ,[object Object],[object Object],Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008
An Ito Process for Stock Prices (See pages 269-71) ,[object Object],[object Object],Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008
Monte Carlo Simulation ,[object Object],[object Object],Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008
Monte Carlo Simulation – One Path (See Table 12.1, page 268) Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008
It ô ’s Lemma (See pages 269-270) ,[object Object],[object Object],Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008
Taylor Series Expansion ,[object Object],Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008
Ignoring Terms of Higher Order Than  t Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008
Substituting for  x Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008
The  2  t Term Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008
Taking Limits Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008
Application of Ito’s Lemma to a Stock Price Process Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008
Examples Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008

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Wiener Process and Ito's lemma process

  • 1. Wiener Processes and Itô’s Lemma Chapter 12 Options, Futures, and Other Derivatives, 7th Edition, Copyright © John C. Hull 2008
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  • 21. Monte Carlo Simulation – One Path (See Table 12.1, page 268) Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008
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  • 24. Ignoring Terms of Higher Order Than  t Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008
  • 25. Substituting for  x Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008
  • 26. The  2  t Term Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008
  • 27. Taking Limits Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008
  • 28. Application of Ito’s Lemma to a Stock Price Process Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008
  • 29. Examples Options, Futures, and Other Derivatives, 7 th Edition, Copyright © John C. Hull 2008