China Redeemable And The Sale Price Of The Bond Duration And Convexity Analysis

The first callable bond in China appeared in 2002 and the first puttable bond in China in 2001. These two kinds of bonds have developed rapidly in China and became important instruments for investors and investees.In this paper, the writer selected yield to maturity of 15-year treasury bonds as interest rate data, and used conditional least squares to estimate the parameters of CIR model. Then, the writer employed Monte Carlo simulation and CIR model to calculate the price, confidence interval, the value of embedded option, option adjusted spread, duration and convexity of 10 callable bonds and 8 puttable bonds in China. The result showed that all these 18 bonds were underestimated by the market, especially the puttable bonds. The coupons of the puttable bonds were too high.When simulated 1000 times, the widths of confidence intervals were between 0.21-0.35 RMB. The average time needed was 744 seconds per bond for callable ones, and 540 seconds per bond for puttable ones, because the average maturity of callable bonds was longer than the one of puttable bonds.According to the result, the duration of the callable bonds and puttable bonds were shorter than the duration of ordinary bonds which had the same clauses but without the callable or puttable clauses. This showed that callable and puttable bonds were less risky. And the convexities of callable bonds were less than the convexity of ordinary bonds, while the convexities of puttable bonds were larger. This result was consistent with theoretical expectations.