There are two ratings in a very simple world: non-default (ND)and default (D).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

Question

There are two ratings in a very simple world: non-default (ND)and default (D).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

Quizplus · Accepted Answer

The Answer is C

There Are Two Ratings in a Very Simple World: Non-Default P=[0.950.0501]P = \left[ \begin{array} { c c } 0.95 & 0.05 \\0 & 1\end{array} \right]P=[0.950​0.051​]

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