# credit risk - marginal default probability

I have been working on an assignment trying to calculate marginal/conditional probability of default. Using a logistic regression framework, I was able to compute the 12-month unconditional PD for each borrower for a duration of four years as shown in the image. For example 0.055 in the image refers to probability of default of borrower 1 during the period 2005 to 2006.

Could someone provide me an insight on how to convert this unconditional probability of default to conditional probability of default. i.e For example, probability of default between 2005 to 2006 given, the borrower has survived till 2005

• Think about Bayes'formula to get your conditionnal probability – DomingoBrown May 2 '18 at 15:35
• Conditional on what? – David Addison May 2 '18 at 19:40
• @ David Addison conditionally on the fact that the company is still alive (not yet defaulted) when you compute that probability – Fr1 Aug 31 '18 at 16:24

The conditional default probability between $t_1$ and $t_2$ is the probability of default between those dates assuming survival until $t_1$. Denoting $\tau$ the default time, this is: $$P(\tau \in [ t_1, t_2 ] | \tau \geq t_1)$$
A simple application of Bayes formula (https://en.m.wikipedia.org/wiki/Bayes%27_theorem) and the fact that $P(\bar{A}) = 1 - P(A)$ will give you the answer from your marginal default probabilities.