Has anyone read this paper? Corporate Yield Spreads Default Risk or Liquidity New Evidence from the Credit Default Swap Market by Longstaff et, al (2005) in Journal of Finance.On footnote 12 the authors mention "As a further identification condition, we require that the estimated values of σ and η be consistent with the volatilities of changes in the estimated λt and γt values." I am not getting how they add this condition when optimizing the values for λt and γt, because the steps are first to estimate their values at each date t (t= 1, ... T), then only after we obtain all values from 1 to T can we compute the volatilities of changes, so I am not sure how to add this constraint in the optimization process for the time t.If you happen to read this paper, please give me some hints, thanks very much in advance.

This is how I understand what they are doing:1, they pick starting parameters2, given the parameters they calculate \lambda_t and \gamma_t for all the 31 observations by minimizing the root mean squared errors at every observation date.3, they calculate the root-mean-squared error between the estimated prices and the true prices through the 31 observation dates (based on foot note 12 they also add the root-mean-squared errors between \sigma and the volatility of changes in the estimated \lambda_t moreover the root-mean-squared errors between \eta and the volatility of changes in the estimated \gamma_t in the optimization criteria) 4, they pick new parameters by some optimization algorithm and go to step 2.I my opinion the econometrics is really weak in this paper (actually this is true for most of Longstaff's papers). The identification of the liquidity process is quite ad hoc.

thanks, 4rcher, your understand is correct, what puzzles me is exactly the third step, do they simple add three RMSE up and minimize the sum? which sounds weird because one RMSE is for prices and the other two RMSE is for volatilities.

Hi tigerbill! I'm also studying this paper! How's your progress? I encountered some problems and hope you can give me some advice. Thank you in advance!My code is written in Matlab. I used the function lsqnonlin to find the best fit of lambda and gamma which result in the smallest SSE. But the answer given by matlab is quite weird. May i know how you tackle this problem? If you'd like, I can also send you my code. Thanks!

Hi tigerbill! I'm also studying this paper! How's your progress? I encountered some problems and hope you can give me some advice. Thank you in advance!My code is written in Matlab. I used the function lsqnonlin to find the best fit of lambda and gamma which result in the smallest SSE. But the answer given by matlab is quite weird. May i know how you tackle this problem? If you'd like, I can also send you my code. Thanks!

Hi Dongni,I am currently studying this paper as well and I am wondering if you solved your matlab issue. I do not fully understand the methodology in the paper. I can fit the CIR model once I obtained the lambdas, but how to I solve for the lambdas? I hope you can help me out. Thanks a lot in advance.