FORMULA1-5536

# FORMULA1-5536 - FINS 5536 Formulas C C 100 y y(1 y N 2 C x...

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1 FINS 5536 Formulas Bond’s cash price: P = (1 + y 2 ) xz x C y C y y N + + 100 1 2 () , and ai = C 2 × x , where z = # of days to next coupon, and x = # of days between coupon payments. U.S. T-bills: P = 100 × [1 nd × 360 ], d = 360 n × [1 P 100 ], where d = discount yield, n = # days to maturity. BEY = 100 P P × 365 n ( n < 365 2 ); BEY = −× × × +− 2 365 365 2 2 365 100 2 365 21 1 1 nn n P n () ( ) ( ) ( n > 365 2 ). P y = C y 2 [1 (1 + y 2 ) N ] + N 2 (100 C y )(1 + y 2 ) ( N + 1) . Δ p = P y × 1 100 , PVBP (per 100% of par) = Δ p × 1 100 , PVBP ( per \$1 million par) = Δ p × 100. D = 2 2 + y y 2 2 12 ++ + yN cy c y y N [( ) ] 1 2 (1 z x ), ( z and x defined as above). Δ P P y Δ y = D × ) 2 / 1 ( y P + Δ y . Δ P P y ×Δ y + 1 2 2 2 y P ×Δ y 2 . Also, Cx = 2 2 P y 1 P 2 2 P y = 2 ) 2 1 ( 4 ) 100 )( 1 ( + + + N y y C N N CN y y N 1 2 + + 2 1 2 1 3 C y y N [( ) ] , D ( p ) = x 1 D (1) + x 2 D (2) + . .. + x m D ( m ), where x i = n i P i / V p . N OTE : in the above equations C = the annual coupon cashflow, while c = the annual coupon rate = C /100 here.

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2 Fisher-Weil Duration: D FW = 1 1 (1 ) N j j j j j C P y = × + . Fisher-Weil Convexity: Cx = 2 1 ) 1 ) N j j j j j jC P y + = + × + . Forward rates: [1 + f 0 ( T 1 , T 2 ) 1 2 ] T T = ) , 0 ( ) , 0 ( 2 1 T b T b = 1 2 ) 1 ( ) 1 ( 1 2 T T y y + + . 1 + y n = [(1 + f 0 (0, 1))(1 + f 0 (1, 2)) × ... × (1 +
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FORMULA1-5536 - FINS 5536 Formulas C C 100 y y(1 y N 2 C x...

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