Continuous time bond pricing coupon bonds

The continuously compounded constant spot rate is r as before. An investor has a choice of purchasing the zero-coupon bond at price P(t, T), which will return the sum of 1 at time T, or of investing this same amount of cash in the money market account, and this sum would have grown to 1 at time T. We know that the value of the money market accoxmt is given by Me If M must have a... 

In 1995 the SNDO launched the second inflation-linked bond, another zero but with a shorter maturity of 10 years (No. 3002, 0% 2004). At this time the SNDO decided to replace the common price anc-tions with multiple price auctions. Moreover, the SNDO opened a noncompetitive facility for small volumes in the auctions, so that small investors could enter the market. In February 1996 the SNDO launched two new bonds a 5-year zero-coupon bond (3003, 0% 2001) and a 12-year coupon bond (3101, 4% 2008). In June 1996 the 24-year coupon bond (3102, 4% 2020) was launched. The market continued to grow rapidly in 1997 and 1998. 

Analysts and researchers frequendy work with logarithms of yields and prices, or continuously compounded rates. One advantage of the logarithmic approach is that it converts the nonlinear relationship expressed in (3-2) into a linear one. The zero-coupon bond price equation in continuous time is... 

In the academic literature, the risk-neutral price of a zero-coupon bond is expressed in terms of the evolution of the short-term interest rate, r t)—the rate earned on a money market account or on a short-dated risk-free security such as the T-bill—which is assumed to be continuously compounded. These assumptions make the mathematical treatment simpler. Consider a zero-coupon bond that makes one payment, of 1, on its maturity date T. Its value at time ris given by equation (3.14), which is the redemption value of 1 divided by the value of the money market account, given by (3.12). 

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