There Are Two Ratings in a Very Simple World: Non-Default $$P = \left[ \begin{array} { c c } 0.95 & 0.05 \\0 & 1\end{array} \right]$$

Multiple Choice

There are two ratings in a very simple world: non-default (ND) and defaultd. The real-world rating transition matrix per year is given by: $$P = \left[ \begin{array} { c c } 0.95 & 0.05 \\0 & 1\end{array} \right]$$ i.e., the probability of defaulting when the current state is non-default is 0.05, and a defaulted bond never leaves that state and has zero recovery. The two-year zero-coupon risk-free rate is 4% (continuously-compounded) . The price of a default-risk-bearing two-year $100 face value zero-coupon bond is $88. If the off-diagonal one-period transition probabilities in the real-world transition matrix are multiplied by a premium adjustment $\pi$ to get the risk-neutral transition matrix (as in the Jarrow-Lando-Turnbull model) , then given the price of the two-year bond, what is the value of $\pi$ ?

A) 1.97
B) 2.00
C) 2.03
D) 2.10