Interest Rate Models and Wiener Processes

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Interest rate models
 
AYESHA AHMAD
 
Vasicek Model
 
 Wiener Processes
 
Vasicek
 
 
 
 
 
 
 
 
GBW
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This content covers the Vasicek model, Wiener processes, exact mean and variance of the model, as well as the geometric Brownian motion. It explains the components and calculations involved in these models with visuals for better comprehension.

  • Interest Rate Models
  • Wiener Processes
  • Vasicek Model
  • Geometric Brownian Motion

Uploaded on Apr 03, 2024 | 1 Views


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Presentation Transcript


  1. Interest rate models AYESHA AHMAD

  2. Vasicek Model Model is given by ?? = ? ?? ?? + ? dWt We need as input ? ? ? ? ? ? and ? to decide ?? =

  3. Wiener Processes Let ? be wiener processes and ?? be the increment ?? in normally distributed with mean zero and variance ?? ?W = ?? (0,1) ?? = ????????? ? Lets define an array W ?[? + 1] = ? [?] + ?? ?? (0,1) ? ? + 1 = ? ? +

  4. Vasicek ?? = ? ?? ?? + ? dWt ?0= 0 Lets define an array R R[? + 1] = R [?] + ??

  5. Exact mean of this model is 1 ? ?? ? ?

  6. Exact variance is ?(1 ?2?? ??? =? ) 2?

  7. GBW ?? = ???? + ???? ? = ?0??? 2?2?? (??2? 1) ??? = ?0

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