5. (5 points) A range bond is a structured security, which can be described as follows. It is like a standard fixed-rate coupon bond, but it pays the coupon at some given time i only if the reference interest rate at time i-l is within a given interval ("the range"). Otherwise, it pays no coupon at that time (but it will pay coupon in the future, if the above-mentioned condition is met). In any case, it will pay the principal back at maturity. Consider now a 3-year range bond, with a coupon equal to i=0 i=1 i=2 $10 per year, and with a principal of $100. The range bond pays the coupon at time i if 12.wu = 0.09 the continuously-compounded 1-year spot rate at time i-1 is within the interval u = 0.06 [0.025,0.05]. Compute the no-arbitrage price 12,ud of the range bond at time i=0, using the To = 0.04 = 0.04 2,04 binomial (continuously-compounded) interest rate tree on the right. The risk-neutral 7.d = 0.03 probability of moving up is 70% in each node. An interval between two movements in the 12.dd = 0.02 tree is A = 1 year. 5. (5 points) A range bond is a structured security, which can be described as follows. It is like a standard fixed-rate coupon bond, but it pays the coupon at some given time i only if the reference interest rate at time i-l is within a given interval ("the range"). Otherwise, it pays no coupon at that time (but it will pay coupon in the future, if the above-mentioned condition is met). In any case, it will pay the principal back at maturity. Consider now a 3-year range bond, with a coupon equal to i=0 i=1 i=2 $10 per year, and with a principal of $100. The range bond pays the coupon at time i if 12.wu = 0.09 the continuously-compounded 1-year spot rate at time i-1 is within the interval u = 0.06 [0.025,0.05]. Compute the no-arbitrage price 12,ud of the range bond at time i=0, using the To = 0.04 = 0.04 2,04 binomial (continuously-compounded) interest rate tree on the right. The risk-neutral 7.d = 0.03 probability of moving up is 70% in each node. An interval between two movements in the 12.dd = 0.02 tree is A = 1 year