ex_7 - ORIE 569 Problem set 7 April 9 2008 Homework must be...

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Unformatted text preview: ORIE 569 Problem set 7 April 9, 2008 Homework must be turned in by Thursday, April 24, at 10 a.m. Solutions turned in at a later time will not be graded. Place homework in the 569 homework box on the bridge between Upson and Rhodes. Exercise 1. a) Show that the dierentia equations CH = 2 2 C 2 + C 1; C (T; T ) = 0; A(T; T ) = 0; and where C H = @C (t; T )[email protected] and AH = @A(t; T )[email protected], have the solutions C (t; T ) = AH = C; sinh( (T t)) 1 cosh( (T t)) + 2 sinh( (T h 1 t)) t)) i : and A(t; T ) = 1 2 2 2 Here = p e 2 (T t) log cosh( (T t)) + 1 sinh( (T 2 2 + 2 2 . b) Use the dierential equations for A and C in Part a) to deduce that the CIR model e satis es the HJM no-arbitrage condition under P. That is, @C (t; T ) @C H (t; T ) @AH (t; T ) @C (t; T ) 2 ( Rt ) + Rt + = Rt C (t; T ); @T @T @T @T see lectures. Exercise 2. Exercise 10.12 on page 459 in Steve Shreve's book. 1 ...
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This note was uploaded on 08/05/2008 for the course ORIE 569 taught by Professor Alexanderschied during the Spring '08 term at Cornell.

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