## Vasicek Model (Interest Rate Drift)

swarnendupathak
Finance Junkie
Posts: 119
Joined: Mon Sep 17, 2012 11:06 am

### Vasicek Model (Interest Rate Drift)

Can u please explain how to convert a non-recombining tree to a recombining tree under Vasicek Model??

swarnendupathak
Finance Junkie
Posts: 119
Joined: Mon Sep 17, 2012 11:06 am

### Vasicek Model (Interest Rate Drift)

is it can be arrived only assessing the probability of UP & DOWN movement last nodal point...by averaging the terminal middle node of of non-recombining tree?? or some other approach is also available?? Please state.

swarnendupathak
Finance Junkie
Posts: 119
Joined: Mon Sep 17, 2012 11:06 am

### Vasicek Model (Interest Rate Drift)

Finance Junkie
Posts: 258
Joined: Thu Sep 20, 2012 3:42 pm

### Vasicek Model (Interest Rate Drift)

Hi i can give you two possible ways here,,,
Vasicek model is,
change in interest rate r= speed of reversion of r*(k-r(t))*small change in time t+ stdDev of r* random error term
if you are taking the up and Down movements as speed of reversion of r*(k-r(t))*small change in time t delta t+ stdDev of r* random error term for up movement and speed of reversion of r*(k-r(t))*small change in time t delta t- stdDev of r* random error term for down movement then i think you shall end up with the recombining tree. A simple non recombining tree has up and down movements governed by the standard deviation oly so that it always converges out but introducing a mean reversion component in these movement shall make the tree recombining i think if i am not wrong.
Converting from the non recombining tree to combining is that you can always know the average time for mean reversion if at all and then stop at the half point of these mean reversion period and then replicate the tree in reverse so that we get two end to end non-recombining trees which represents a recombining trees now

Finance Junkie
Posts: 258
Joined: Thu Sep 20, 2012 3:42 pm

### Vasicek Model (Interest Rate Drift)

It describes the movement of an interest rate as a factor of , time , equilibrium value and market risk .
The Vasicek interest rate model values the instantaneous interest rate using the following equation:

drt = a(b-rt)dt +sdWt

Random market movements affect the moments of interest rates . This model is called the Vasicek interest rate model.

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