The process for the prices of a 5-year maturity zero-coupon bond and of a derivative on...

Transcribed Image Text:

The process for the prices of a 5-year maturity zero-coupon bond and of a derivative on the interest rate that matures in three years are decribed by the following trees. The probablities that an analyst associates with going up and down are 60% and 40% at each node of the tree, respectively. (NOTE: These are NOT the risk neutral probabilities.) period time (in years) i=0 t = 0 Zo 52.03 5-year zero coupon bond price i=1 i=2 i 3 i 4 t = 1 t = 2 t = 3 t = 4 Z Z2 Z 55.55 63.08 61.81 67.07 74.84 70.91 75.49 79.05 86.57 84.33 87.02 89.12 91.31 95.86 i 5 t = 5 100 100 100 100 100 100 period time (in years) Derivative i=0 i 1 t=0 t = 1 40.33 68.04 23.92 i=2 t = 2 108.72 49.17 4.64 i=3 t = 3 154.5 103 10.3 0 1. Suppose that you hold a portfolio of 10 five-years zeros and 20 derivatives. How does the portfolio payoff evolve over three years? Construct the tree. 2. How can you change your position in the derivative in order to make the portfolio riskless between date t = 0 and t = 1? 3. What is the implied interest-rate tree up to t = 2? 4. What is the price of a zero-coupon bond that matures at time t = 2? The process for the prices of a 5-year maturity zero-coupon bond and of a derivative on the interest rate that matures in three years are decribed by the following trees. The probablities that an analyst associates with going up and down are 60% and 40% at each node of the tree, respectively. (NOTE: These are NOT the risk neutral probabilities.) period time (in years) i=0 t = 0 Zo 52.03 5-year zero coupon bond price i=1 i=2 i 3 i 4 t = 1 t = 2 t = 3 t = 4 Z Z2 Z 55.55 63.08 61.81 67.07 74.84 70.91 75.49 79.05 86.57 84.33 87.02 89.12 91.31 95.86 i 5 t = 5 100 100 100 100 100 100 period time (in years) Derivative i=0 i 1 t=0 t = 1 40.33 68.04 23.92 i=2 t = 2 108.72 49.17 4.64 i=3 t = 3 154.5 103 10.3 0 1. Suppose that you hold a portfolio of 10 five-years zeros and 20 derivatives. How does the portfolio payoff evolve over three years? Construct the tree. 2. How can you change your position in the derivative in order to make the portfolio riskless between date t = 0 and t = 1? 3. What is the implied interest-rate tree up to t = 2? 4. What is the price of a zero-coupon bond that matures at time t = 2?

Answer rating: 100% (QA)

1 To construct the portfolio payoff tree over three years we need to consider the values of the zeros and derivatives at each time period At t0 The va... View the full answer