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The pricing of credit-sensitive bonds, that is, bonds which have a significant probability of default, is an issue of increasing academic and practical importance. The recent practice in financial markets has been to issue high yield corporate bonds that are a hybrid of equity and risk-free debt. Also, to an extent, most corporate bonds are credit-sensitive instruments, simply because of the limited liability of the issuing enterprise. In this paper, we suggest and implement a model for the pricing of options on credit-sensitive bonds. For example, the model can be used to price call provisions on bonds, options to issue bonds, and yield-spread options. From a modelling. | Debt Instruments and Markets Professor Carpenter Yield to Maturity Outline and Suggested Reading Outline Suggested reading Yield to maturity on Veronesi Chapter 2 bonds Tuckman Chapter 3 Coupon effects Par rates Buzzwords Internal rate of return Yield curve Term structure of interest rates Yield to Maturity 1 Debt Instruments and Markets Professor Carpenter Definition of Yield Suppose a bond or portfolio of bonds has price P and positive fixed cash flows K1 K2 . Kn at times t1 t2 . tn. Its yield to maturity is the single ratey that solves Kn p 1 y 2 2 1 1 y 2 2 2 1 y 2 2 or n K. l y 2 2 p Note that the higher the price the lower the yield. Example Recall the 1.5-year 8.5 -coupon bond. Using the zero rates 5.54 5.45 and 5.47 the bond price is 1.043066 per dollar par value. That implies a yield of 5.4704 0.0425 0.0425 1.0425 1 0.0554 2 1 1 0.0545 2 2 1 0.0547 2 3 1.043066 _ 0 0425 0 0425 1 0425 1 0.054704 2 1 1 0.054704 2 2 1 0.054704 2 3 Yield to Maturity 2 Debt Instruments and Markets Professor Carpenter Yield of a Bond on a Coupon Date For an ordinary semi-annual coupon bond on a coupon date the yield formula is where c is the coupon rate and T is the maturity of the bond in years. Annuity Formula Math result y_1 _X 1 1 1 y 2 s y 2 1 y 2 Finance application This formula gives the present value of an annuity of 1 to be received every period for n periods at a simply compounded rate of r per period. Yield to Maturity
