Relationship between default risk and value of bond In particular Mortgage-backed securities. I've read from a book that underestimating the risk of default is tantamount to overestimating the value of the bond, giving rise to a bubble in MBS. I'm unclear of how that works. 
My guess is that since the probability of default risk is low, thus banks give out lower coupon rates. Investors buy MBS up because they are safer, demand for MBS increase, price of these MBS pushed up.
[...] underestimating the risk of default is tantamount to overestimating the value of the bond.


The reason behind this is simply due to how bonds are priced.

$$
P = \sum_{n=1}^N \frac{C + M[{I_{n=N}}]}{(1+i)^n}
$$

Where $i$ is the contractual interest rate, $C$ is the coupon payment, $N$ is the number of payments, $I_{n=N}$ is an indicator function taking the value of $1$ when $n=N$ is $true$ or $0$ otherwise, $P$ is the market price of the bond, $M$ is the value of the bond at maturity.

When $i$ goes up, $P$ goes down and vice versa, see



$\rightarrow$ if $i$ is underestimated, $P$ will be overestimated. Indeed, it is $i$ which, via a premium, internalizes the default risk consideration and is an increasing quantity of it.