assignmnt3-3

assignmnt3-3 - (d Compute the Arrow-Debreu prices A t n t =...

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ACTSC445/845 ASSIGNMENT 3. DUE ON MONDAY, JULY, 5TH BEFORE CLASS In this assignment, you are asked to write a program (prob- lem 2), you can either use matlab or excel for the program- ming. A drop box has been created for you to submit the electric ±les. (1) [20 points] Consider the following binomial tree, where q ( t, n )= 0 . 4 for all nodes ( t, n ), and one period is equal to one year. i (3 , 3) = 8% i (2 , 2) = 7% i (3 , 2) = 6% i (1 , 1) = 6% i (2 , 1) = 5% i (3 , 1) = 4% i (0 , 0) = 5% i (1 , 0) = 4% i (2 , 0) = 3% i (3 , 0) = 2% Answer the following parts based on the above short rate lattice: (a) Compute the implied 1-year, 2-year and 3-year spot rates of interest. (b) Use backward recursion to price a 4-year coupon bond with 100 face value and annual coupon rate of 5% payable an- nually. (c) Use backward recursion to price a 2-year Foor with Foor rate 5% payable in advance, $1,000 notional amount and reset annually.
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Unformatted text preview: (d) Compute the Arrow-Debreu prices A ( t, n ), t = 0 , ..., 3, n = , ..., t . (e) Demonstrate how you could use the Arrow-Debreu prices in part 1d to compute directly the prices of the Foor of part 1c. (2) [20 points] Assume that initially all interest rates are 6% per year and that the term structure of the volatilities (in % per year) of the short rate for term t (in years) is: σ ( t ) = 15-Date : June,16, 2010. 1 2ACTSC445/845 ASSIGNMENT 3. DUE ON MONDAY, JULY, 5TH BEFORE CLASS t 2 . Write a program to compute a 10-year Black-Derman-Toy interest rate lattice with yearly time steps. Using your model to price a callable bond which has the following features (a) face value is 100, (b) coupon rate is 3%, (c) the bond is callable starting from time 5. (at the beginning of 6 year.)...
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assignmnt3-3 - (d Compute the Arrow-Debreu prices A t n t =...

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