Understanding Interest Rate Models and Wiener Processes

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.

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

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Uploaded on Apr 03, 2024 | 1 Views

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 [?] + ??

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

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

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