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W09hw6 - Math 623 F 2011 Homework 6 For full credit your...

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Math 623, F 2011: Homework 6. For full credit, your solutions must be clearly presented and all code included. (1) This problem is concerned with calculations on the Hull-White tree constructed in problem 3 of homework V. You should use spline interpolation and the Hull-White value for J . (a) Using the Monte-Carlo method, estimate the probability p n ( T ) that the inter- est rate r ( t ) < 0 for some t T . Do this for n = 2 , ... 6, and T = 12. Use N = 10 5 simulations in the MC implementation. (b) Plot on the same axes the graphs of p n ( T ) , 0 T 12 for n = 2 , 3 , 4. (c) Using the Monte-Carlo method, estimate the value of an interest rate cap (on a notional principle of 100) for a 12 year floating rate loan where the cap is 6% annual rate, with payment of interest 8 times per annum. Use N = 10 5 simulations in the MC implementation. (d) Estimate the value of the cap in (c) using the finite difference method. (2) This problem is also concerned with calculations on the Hull-White tree constructed in problem 3 of homework V. You should use the finite difference method (as
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