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term_stru_summary

term_stru_summary - U NIVERSITY OF E SSEX D EPARTMENT OF E...

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U NIVERSITY OF E SSEX D EPARTMENT OF E CONOMICS Term Structure of Interest Rates Yield curves Yield curves show the relationship between spot yield and time to maturity (i.e. ‘life’) of a bond. Spot yield : y n,t ( m/p n,t ) (1 /n ) - 1 is the yield to maturity on a Zero Coupon (pure discount) bond with life n at date t , where p n,t is the market price of the bond at date t and m is its face value. From now on all bonds are assumed to be Zero Coupon. Theories of the term structure seek to explain the shape of the yield curve at each date. Implicit forward rates Implicit forward rates are future yields (interest rates) implied by today’s observed bond yields. Define n - 1 f n as the implied rate between dates n - 1 and n as of today, t : (1 + y n - 1 ) n - 1 (1 + n - 1 f n ) = (1 + y n ) n (1) All the above are defined as of today, i.e. should have an extra t subscript. The term structure (yield curves) can equivalently be expressed using implicit forward rates, rather than spot yields.
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