Given the 1-period forward rates of 3%, 4%, and 5% for year 1, 2 , and 3, and an interest rate volatility of 10%,

1. Calibrate a binomial interest rate tree, taking into account of the interest rate volatility, and assuming that higher and lower forward rates for future periods are related by:

1,= 0R_(1,H)=Implied forward rate at time 0e^,

1,= 0 R_(1,L)=Implied forward rate at time 0 e^(-),

And therefore: 1,= 1,2R_(1,H)= R_(1,L) e^2, 2,= 2,4, 3,= 3,6,R_(2,HH)= R_(2,LL) e^4, R_(3,HHH)= R_(3,LLL) e^6,

2. Use the binomial interest rate tree, assuming that forward rates could go up with a 60% probability and go down with 40% probability, to compute the price for a 3-year, 6%, $100 face value bond which is putable at the end of year 2 and year 3, at a put price of $99.