Suppose that you are given the following Ho-Lee interest rate tree 0.01005 -0.02891 -0.06964 0.01177 -0.05216 -0.03482 t = 0 t = 0.5 t=1 All interest rates are annual, but semi-annually compounded. Suppose that you are also told that a 1yr zero-coupon bond is worth $98.50 and a 1.5yr zero-coupon bond is worth $96. Use $100 notionals and face values throughout the problem. The first interest rate, 0.01005, has already been locked-in in determining the first payment in floating rate bonds and other securities whose payoffs depend on the prevailing interest rate. a) What is the value of a 1.5-year cap where payments are made six months after interest reset dates and the strike is 4%? d) What is the value of a 1.5-year floor where payments are made six months after interest reset dates and the strike is 4%? (e) The modified duration of the cap in (a) is -54.4244 (for annual interest rates). Does this mean that the cap value goes up or down with interest rates? Explain why this makes sense. (f) What is the modified duration of the capped floating rate bond in (c)? Suppose that you are given the following Ho-Lee interest rate tree 0.01005 -0.02891 -0.06964 0.01177 -0.05216 -0.03482 t = 0 t = 0.5 t=1 All interest rates are annual, but semi-annually compounded. Suppose that you are also told that a 1yr zero-coupon bond is worth $98.50 and a 1.5yr zero-coupon bond is worth $96. Use $100 notionals and face values throughout the problem. The first interest rate, 0.01005, has already been locked-in in determining the first payment in floating rate bonds and other securities whose payoffs depend on the prevailing interest rate. a) What is the value of a 1.5-year cap where payments are made six months after interest reset dates and the strike is 4%? d) What is the value of a 1.5-year floor where payments are made six months after interest reset dates and the strike is 4%? (e) The modified duration of the cap in (a) is -54.4244 (for annual interest rates). Does this mean that the cap value goes up or down with interest rates? Explain why this makes sense. (f) What is the modified duration of the capped floating rate bond in (c)