Vasicek model

[intuitive]

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

 

[ShaktiRathore]

Hi i can give you two possible ways if you agree
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.
thanks

 

[intuitive]

Much aprreciated
thanks ShaktiRathore

 

[tosuhn]

hihi @ShaktiRathore was wondering if you can help me here. I am reading the notes on Vasicek and the highlighted portion seems incomplete.
Appreciate your help

regards,
sun

 

[ShaktiRathore]

Hi,
the missing letter i think is k. Because in the model k-r(t) is the only difference term and also the difference seems to be positively related to the the change in interest rates. Therefore greater the difference between r and k greater should be the expected change in the shorter term rate. You just look at the magnitude not the sign because change in interest rate is high either way provided difference k-r(t) is large enough.
thanks

 

[tosuhn]

Hi @ShaktiRathore thanks for your reply.
The formula presented in the notes is dr= k*(theta-r)dt + (sigma)dw. Will it be the difference between r and theta instead?
Hope to hear from you soon

Thanks again.
Regards,
Sun

 

[ShaktiRathore]

Yes its theta.
Thanks