PROBLEM ESTIMATE PARAMETERS CIR COX INGERSOLLL ROS

[manuelito]

I need some help with pricing of ZCB under CIR.
CIR model: d r=a∗(b − r)dt+σ√r dW,
we know that to price a ZCB we have to change probability and we opteined:
dr=â∗(b^ − r)dt+σ√r dW (under Q probability risk-neutral), where â=a +σλ and b^=a*b/(a+σλ), λ is a costant.
My question is: how can I estimate â (b^ doesen't metter because is a function of â and λ) and λ ? with data i can estimated , a, b and σ
Thank you

 

[cycbill]

One would obtain a set of zero-coupon bond prices (with different maturities) quoted from the market.
And then set up the ZCB pricing formula from CIR model.
Finally, best fit the ZCB market prices with the model (e.g. using least square mean), to estimate these parameters.

 

[manuelito]

One would obtain a set of zero-coupon bond prices (with different maturities) quoted from the market.
And then set up the ZCB pricing formula from CIR model.
Finally, best fit the ZCB market prices with the model (e.g. using least square mean), to estimate these parameters.

Thank for answer, but is not what I ask. I try to explain better.
My goal is simulate price of zcb, to do this know from letterature that B(t, T) (price of zcb) is equal to exp(-A(t, T) - C(t, T) r(t)). Under CIR function C and A use â as parameters, and my question is how can estimate this parameter

 

[Paul Lopez]

Thank for answer, but is not what I ask. I try to explain better.
My goal is simulate price of zcb, to do this know from letterature that B(t, T) (price of zcb) is equal to exp(-A(t, T) - C(t, T) r(t)). Under CIR function C and A use â as parameters, and my question is how can estimate this parameter

Maximum Likelihood Esimation is going to be your best friend here. This is the most common method for estimating the parameters of the CIR model. You would write down the likelihood function for the CIR model given some observed interest rate data and then find the parameter values that maximize this function. The likelihood function is typically derived from the transition density function of the CIR process. Python and R have built-in functions to help with this. SciPy in python is very user friendly.