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as1_sol - Columbia University M.S. in Financial Engineering...

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Unformatted text preview: Columbia University M.S. in Financial Engineering IEOR 4706: Foundations of Financial Engineering Instructor: Rama CONT Summer 2011. TA: Jinbeom Kim Assignment 1. Bond pricing. Assignments should be done individually. The table below shows the term structure of (annually compounded) US Treasury interest rates on t = July 12, 2010 and t 1 = July 12, 2011. Let T = { 0.5, 2, 3, 5, 10, 30 } . R t ( T, T + 1) denotes the (annually compounded) forward rate fixed at date t for the period [ t + T, t + T + 1]. D ( t, T + t ) denotes the discount factor at t for maturity T . Maturity 6 m 2 3 5 10 30 yr July 12, 2010 0.08 % 0.40 % 0.70 % 1.56% 2.97% 4.18% July 12, 2011 0.05 % 0.35% 0.58 % 1.43% 2.88 4.17 All the asnwers are included in Assignment1.m file. 1. Assuming that the forward rates are piecewise constant between any two maturities in T , compute and plot the corresponding (discretely compounded) forward rates R t ( T, T + 1) and R t 1 ( T, T + 1) , T = 1 , .. 29. What is R t (0 , 1)? (Answer) See ForwardRate.m file for codes. Let’s define T = 0, T 1 = 0.5, T 2 = 2, T 3 = 3, T 4 = 5, T 5 = 10, and T 6 = 30. Since (1 + R t ( T , T i +1 )) T i +1- T = (1 + R t ( T , T i )) T i- T · (1 + R t ( T i , T i +1 )) T i +1- T i , the forward rate between T i and T i +1 is R t ( T i , T i +1 ) = ( (1 + R t ( T i , T i +1 )) T i +1- T (1 + R t ( T i , T i +1 )) T i- T ) 1 T i- T i...
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This note was uploaded on 03/14/2012 for the course IEOR 4706 taught by Professor Stevenkou during the Fall '10 term at Columbia.

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as1_sol - Columbia University M.S. in Financial Engineering...

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