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设债券的面值为 M,票面利率为 r,尚有 n年到期 ,市场利率为 k,刚支付利息后债券的价值 V=V( k,n) ,其关于 k的偏导数的绝对值记为 P( k,n) ,a=( 1 + k) /( k- r)。可证 :定理 1 设 n2 n1,当有下列情况之一时 :1 ) r≥ k,2 ) kr,n1a,3) kr,有 n0 a使得 P( k,n0 ) Mr/k2 ,
Suppose the face value of a bond is M, the coupon rate is r, there are n years maturity, the market interest rate is k, the value of the bond just after paying interest V = V (k, n), its absolute value of k Is P (k, n), a = (1 + k) / (k-r). Theorem 1: Suppose n2 n1, when there is one of the following conditions: 1) r ≧ k, 2) kr, n1a, 3) kr and n0 a such that P (k, n0) Mr / k2,