# NPV of a mortage loan

I need to model the expected NPV of a mortage loan over his whole life-time. Assume that only the prepayment and default risk matters and that these events can occour at only discrete time-points. I'm not shure whethere to use conditional probabilities - cunditioned on having survived up to the payment date or "unconditional" ones.

Option 1: $E(NPV)=\sum_t \frac{1}{(1+r)^t} ( P(T=t,prepayment) CF^{pre}+ P(T=t,default) CF^{def}+ P(T=t,regular) CF^{reg})$

Option 2:

$E(NPV)=\sum_t \frac{1}{(1+r)^t} ( P(T=t,prepayment|T>=t) CF^{pre}+ P(T=t,default|T>=t) CF^{def}+ P(T=t,regular|T>=t) CF^{reg})$

Where T denotes the stochastic variable, modelling the discrete timepoints at which the payments are expected.

Do you have a reference/textbook on which option to choose?

Or do I even miss an option?