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【正文】 Hull Par Yield continued In general if m is the number of coupon payments per year, d is the present value of $1 received at maturity and A is the present value of an annuity of $1 on each coupon date Amdc )1 0 01 0 0( ??Options, Futures, and Other Derivatives, 5th edition 169。 20xx by John C. Hull Sample Data for Determining the Zero Curve (Table , page 97) Bond Time to Annual Bond Principal Maturity Coupon Price (dollars) (years) (dollars) (dollars) 100 0 100 0 100 0 100 8 100 12 Options, Futures, and Other Derivatives, 5th edition 169。 20xx by John C. Hull The Bootstrapping the Zero Curve ? An amount can be earned on during 3 months. ? The 3month rate is 4 times % with quarterly pounding ? This is % with continuous pounding ? Similarly the 6 month and 1 year rates are % and % with continuous pounding Options, Futures, and Other Derivatives, 5th edition 169。 20xx by John C. Hull The Bootstrap Method continued ? To calculate the year rate we solve to get R = or % ? Similarly the twoyear rate is % 9610444 ??? ?????? ReeeOptions, Futures, and Other Derivatives, 5th edition 169。 20xx by John C. Hull Zero Curve Calculated from the Data (Figure , page 98) 91011120 0 .5 1 1 .5 2 2 .5Zero Rate (%) Maturity (yrs) Options, Futures, and Other Derivatives, 5th edition 169。 20xx by John C. Hull Forward Rates The forward rate is the future zero rate implied by today’s term structure of interest rates Options, Futures, and Other Derivatives, 5th edition 169。 20xx by John C. Hull Calculation of Forward Rates Table , page 98 Zero Rate for Forward Rate an n year Investment for n th Year Year ( n ) (% per annum) (% per annum) 1 2 3 4 5 Options, Futures, and Other Derivatives, 5th edition 169。 20xx by John C. Hull Formula for Forward Rates ? Suppose that the zero rates
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