= --TF, (4) In finance, a zero coupon bond is a contract that pays out one dollar at maturity. The problem is how much m

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Tf 4 In Finance A Zero Coupon Bond Is A Contract That Pays Out One Dollar At Maturity The Problem Is How Much M 1 (85.96 KiB) Viewed 33 times

= --TF, (4) In finance, a zero coupon bond is a contract that pays out one dollar at maturity. The problem is how much money should one pay at time t to receive a dollar at time T? Here t <T and T is the maturity of the bond. Different pricing models exist. In the Cox, Ingersoll and Ross (CIR) model, the price P(t,T,r) of a zero coupon bond at time t, maturing at T is given by P(t, T,r) = F(T-t, r;0) where F(t,r; 2) satisfies the PDE aF 1 2-F ar or + (a - br) at 2 ar2 ar subject to F(0,r; 2) = e-fr. In this equation r represents the so called spot rate of interest. To solve this, look for a solution of the form F(t,r; 4) = -a$(t)-relt) and show that we must have (0) = 0, 7(0) = X and (0.1) o(t) = v(t). (0.2) Solve the Riccati equation for and hence derive a formula for the price of a zero coupon bond in the CIR framework. The integral to obtain o from y can be done in Mathematica. =e = - 4'(t) = 20°'®(t) + by(t) – 1 =