CreditGrades model calibration and initial values

Currently doing a project on structural models, and I want to apply the CreditGrades model. My question is what values are the parameters going to take, in order to update the implied probability of default every trading day. My initial thought:

Assume we are at time $t=n$: We use as input $S_0= S_n$ and $S^* = S_n$ and $\sigma^*_s = STDEV.S(n,n-252)*SQRT(252)$

At time $t=n+1$: We use as input $S_0= S_{n+1}$ and $S^* = S_{n+1}$ and $\sigma^*_s = STDEV.S(n+1,n+1-252)*SQRT(252)$

$\vdots$

At time $t=n+k$: We use as input $S_0= S_{n+k}$ and $S^* = S_{n+k}$ and $\sigma^*_s = STDEV.S(n+k,n+k-252)*SQRT(252)$

I am not sure , finanally , whether $S_0$ should be fixed as the stock price in the end of the previous fiscal year, (Stock price at 31/12/20X0)

Note: $STDEV.S(n,n-252)$ is the standard deviation of the daily log returns for 252 trading days. Each new trading day we erase the last value with the return of the day we are at the moment. The technical document suggests a 1000day estimator for the standard deviation but due to absence of data I use 252day estimator.

Source: Finger, C, Finkelstein, V, Pan, G, Lardy, JP and Tiemey, J. 2002. “CreditGrades Technical Document”. In RiskMetrics Group