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# hw6 - Math 623 W 2007 Homework 6 For full credit your...

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Math 623, W 2007: Homework 6. For full credit, your solutions must be clearly presented and all code included. In this homework you will calibrate two fixed income (short rate) models to real (but not current) data. The following table gives the yields of zero coupon bonds, computed using annual compounding, for various maturities. The table also gives the market implied (flat) volatilies of at-the-money caps. Maturity Yield Volatility 0 0.0480 1 0.0454 0.1520 2 0.0456 0.1620 3 0.0462 0.1640 4 0.0471 0.1630 5 0.0481 0.1605 7 0.0502 0.1555 10 0.0526 0.1475 15 0.0556 0.1350 20 0.0575 0.1260 Each cap can be described as follows. Consider dates 0 < T 0 < T 1 < · · · < T n = T with T i = 3( i +1) months. The cap pays ( T i - T i - 1 )( L ( T i - 1 , T i ) - R ) + at time T i for i = 1 , . . . , n , where R = R ( T ) is the swap rate and L ( T i - 1 , T i ) the LIBOR rate. The terminal time T is the maturity listed in the table. The implied cap volatilities come from Black’s formula. (1) (a) Compute the price p (0 , T ) today of the zero coupon bond maturing at T for 0 T 20. Use linear interpolation on the yields to do this. Display your result in a plot of p (0 , T ) vs T .

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hw6 - Math 623 W 2007 Homework 6 For full credit your...

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