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:

probability of call

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

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


  • 2
    $\begingroup$ 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 $V$. $\endgroup$ Sep 29 at 7:16
  • $\begingroup$ 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? $\endgroup$
    – samael
    Sep 29 at 9:54

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