# Question on estimating the probability of a bond being called

I'm doing a research on estimating the probability of a bond being called and found Sarkar's (2001) paper where a formula for this was derived using Ito's lemma as seen below:

I have very little background in partial differential equations so I don't understand or could not find in the paper what and represents. Can anyone help me understand what are these?

I have included a link to the paper in case anyone is interested.

http://directory.umm.ac.id/Data%20Elmu/jurnal/J-a/Journal%20Of%20Banking%20And%20Finance/1542.pdf

• I just read briefly the paper. From what I understood, the author is trying to find the probability of calling's dynamics. In his notation $P_t$ should be the derivative of the probability with respect to time. $P_V$ the derivative of the probability with respect to the underlying firm value. $P_{VV}$ the second derivative wrt $V$. Sep 29 at 7:16
• Thanks for taking the time to look into this. May I ask for your help on how can I derive the values for these variables? Sep 29 at 9:54