Now given the following information with expected to possible movements of rates, please value the following bonds? Each arrow represents a probability of $50\%$ at point of intersection Use that information to value the following bonds. All possible rate paths have a $50\%$ probability at each point. $1)$ You are looking at a callable bond with par value of $$1$ million which is callable starting at year $1.$ The bond has a $3$ year maturity and has a coupon of $5\%$ and has a bullet maturity due in $3$ years unless it is called between year $1$ and year $3.$ The bond is callable at par should issuer choose to exercise option.

a$.$ What is value of the bond without call and what is value of bond with call?

b$.$ What is implied value of the call?

$2)$ Value a putable bond with par value of $$1$ million which is putable starting at year $1.$ The bond has a $3$ year maturity and has a coupon of $5\%$ and has a bullet maturity due in $3$ years unless it is put back to issuer between year $1$ and year $3?$ The bond is putable at par should investor choose to exercise option.

a$.$ What is value of the bond without put and what is value of bond with put?

b$.$ What is implied value of the put?