15A 4 + 4 + 4 + 4 Suppose we have zero coupon bonds of maturities of 1, 2 and 3 years, and a money market account as shown below. time-> state-> B(1) B(2) B(3) mma 0 up down 0.97 1 0.93 0.9620 0.9555 0.88 0.9167 ? 1 1.0309 1.0309 a) State the condition for the tree to be free of arbitrages. b) What should be the value of B(3) at time 1 in the down state to rule out arbitrages ? c) What is the payoff to the holder of a caplet maturing at time 1 with a strike of 3% and a notional of $10 mn 2 d) What should be the price of the caplet at time 0? or 15B 4 + 4 + 4 + 4) a) How does the Ho-Lee model get the flexibility to fit any initial term structure? b) Why do we need multi-factor models? Based on your assignment, what factors contribute most of the variation in changes in interest rates ? c) Suppose we have X and Y which have zero mean, unit variance and correlation 0.5. Identify their principal components U and V in terms of X and Y. d) How many unique sources of risk does the GAUSS+ model have? Why is it called a cascade model? 15A 4 + 4 + 4 + 4 Suppose we have zero coupon bonds of maturities of 1, 2 and 3 years, and a money market account as shown below. time-> state-> B(1) B(2) B(3) mma 0 up down 0.97 1 0.93 0.9620 0.9555 0.88 0.9167 ? 1 1.0309 1.0309 a) State the condition for the tree to be free of arbitrages. b) What should be the value of B(3) at time 1 in the down state to rule out arbitrages ? c) What is the payoff to the holder of a caplet maturing at time 1 with a strike of 3% and a notional of $10 mn 2 d) What should be the price of the caplet at time 0? or 15B 4 + 4 + 4 + 4) a) How does the Ho-Lee model get the flexibility to fit any initial term structure? b) Why do we need multi-factor models? Based on your assignment, what factors contribute most of the variation in changes in interest rates ? c) Suppose we have X and Y which have zero mean, unit variance and correlation 0.5. Identify their principal components U and V in terms of X and Y. d) How many unique sources of risk does the GAUSS+ model have? Why is it called a cascade model