as2_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. Assignment 2. Forward rate agreements and swaps. Solution by: Rama Cont The tables below display USD LIBOR and swap rates on July 14, 2011. (Source: US Federal Reserve Board). The swap rates correspond to swaps with annual xed payments and semi-annual oating payments based on 6-month LIBOR. Maturity 1 m 3 m 6 m 1 year LIBOR Rate (%) 0.1865 0.2498 0.4165 0.43 % USD Swap and LIBOR Rates on July 14, 2011. Maturity (years) 1 2 3 4 5 7 10 30 Swap rates (%) 0.43 0.62 0.97 1.39 1.80 2.45 3.05 3.89 t = 0 denotes July 14, 2011. We denote T = f : 5 k;k = 1 ::: 60 g . The discount factors for T 1 year are given by D (0 ;T ) = 1 = (1 + T L ( T )) where L ( T ) is the LIBOR rate for maturity T : Maturity 1 m 3 m 6 m 1 year D (0 ;T ) 0.9998 0.9994 0.9979 0.9957 1. What is the forward LIBOR rate for the period starting on Aug 14, 2011 and ending on Oct 14, 2011? Answer: Recall that the forward LIBOR rate is given by F ( T;T + ) = 1 ( D (0 ;T + ) D (0 ;T ) 1) Here T = 1 = 12 ;T + = 0 : 25 ; = 1 = 6 so, using the 1 month and 3 month LIBOR rates to compute the discount factors we get F ( 1 12 ; : 25) = ( 1 + 0 : 25 L (0 : 25) 1 + 1 12 L ( 1 12 ) 1) 6 = 0 : 2814% (1) 2. An annuity issued by Gadol Bank, with notional 1 M$, and annual coupon rate c = 3%, has two remaining payments on Oct 14 and Jan 14, 2011.= 3%, has two remaining payments on Oct 14 and Jan 14, 2011....
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as2_sol - Columbia University M.S. in Financial Engineering...

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