Le Philippe: Case Study
CASE STUDY “LE PHILIPPE”
Question1: Describe all the possible outcomes:
As the following graph shows, from up to down, there are totally 6 possible outcomes depending on whether strike the put option or not and how to determine the new coupon rate at 2017 and 2020 respectively.
Question2: Calculate the spot rate
We can calculate the spot rate according to 1-5 year spot rate and the available 6-10 coupon rate by bootstrapping. We do not have the available 6-9 year spot rate, since the case has offered us the AAA treasury coupon rate which could be further considered as risk free. So we could use bootstrapping method to get the 6-9 theoretical default-free yield.(sheet spot rate)
Maturity 1 2 3 4 5 6 7 8 9
Spot 0.75% 1.25% 1.75% 2.00% 2.10% 2.18% 2.30% 2.36% 2.37%
Question3: generate the spot rates using a term structure
We choose to use the Ho-Lee model. First step, we use the spot rate calculated in Q2 to get the risk-free bond’s market prices .Then, we calculate the volatility by using the spot rates in 1995(sheet volatility), and use it as the volatility today. As the teacher showed us, we firstly try a set of theta in order to generate an binominal tree, then we get the risk-free bonds’ model prices. With the help of Excel, we minimize the sum of squares of the difference between the model price and the market price by adjusting the a set of theta. Finally, we get the real binominal tree.(sheet Ho-Lee model) Question4: show how to value market interest rate prevailing at that date(think of floating rate bond )
Because the floating rate bond is always at par, the coupon rate equal to the market interest rate.
Question5: show how to decompose the “Phillipe” in bonds + options
The “Phillipe” could be made up by an option-free bond plus 2 options- 2017 put option and 2020 put option. in 2017, investors have 2 choices: 1) if the bond price is less than 100, they will use the put option to sell the bond at par; 2)if the bond price
Question1: Describe all the possible outcomes:
As the following graph shows, from up to down, there are totally 6 possible outcomes depending on whether strike the put option or not and how to determine the new coupon rate at 2017 and 2020 respectively.
Question2: Calculate the spot rate
We can calculate the spot rate according to 1-5 year spot rate and the available 6-10 coupon rate by bootstrapping. We do not have the available 6-9 year spot rate, since the case has offered us the AAA treasury coupon rate which could be further considered as risk free. So we could use bootstrapping method to get the 6-9 theoretical default-free yield.(sheet spot rate)
Maturity 1 2 3 4 5 6 7 8 9
Spot 0.75% 1.25% 1.75% 2.00% 2.10% 2.18% 2.30% 2.36% 2.37%
Question3: generate the spot rates using a term structure
We choose to use the Ho-Lee model. First step, we use the spot rate calculated in Q2 to get the risk-free bond’s market prices .Then, we calculate the volatility by using the spot rates in 1995(sheet volatility), and use it as the volatility today. As the teacher showed us, we firstly try a set of theta in order to generate an binominal tree, then we get the risk-free bonds’ model prices. With the help of Excel, we minimize the sum of squares of the difference between the model price and the market price by adjusting the a set of theta. Finally, we get the real binominal tree.(sheet Ho-Lee model) Question4: show how to value market interest rate prevailing at that date(think of floating rate bond )
Because the floating rate bond is always at par, the coupon rate equal to the market interest rate.
Question5: show how to decompose the “Phillipe” in bonds + options
The “Phillipe” could be made up by an option-free bond plus 2 options- 2017 put option and 2020 put option. in 2017, investors have 2 choices: 1) if the bond price is less than 100, they will use the put option to sell the bond at par; 2)if the bond price