TAILIEUCHUNG - Coupon Bonds and Zeroes

There are two principal approaches to the modelling of credit-sensitive bond prices. Merton (1977)’s structural approach, recently re-examined by Longstaff and Schwartz (1995), prices corporate bonds as options, given the underlying stochastic process assumed for the value of the firm. On the other hand, the reduced form approach, used in recent work by Duffie and Singleton (1999) and Jarrow, Lando and Turnbull (1997), among others, assumes a stochastic process for the default event and an exogenous recovery rate. Our model is a reduced-form model that specifies the credit spread as an exogenous variable. Our approach follows the Duffie and Singleton ”recovery of market value” (RMV) assumption. As. | Debt Instruments and Markets Professor Carpenter Coupon Bonds and Zeroes Concepts and Buzzwords Coupon bonds Zero-coupon bonds Bond replication No-arbitrage price relationships Zero rates Zeroes STRIPS Dedication Implied zeroes Semi-annual compounding Reading Veronesi Chapters 1 and 2 Tuckman Chapters 1 and 2 Coupon Bonds and Zeroes 1 Debt Instruments and Markets Professor Carpenter Coupon Bonds In practice the most common form of debt instrument is a coupon bond. In the and in many other countries coupon bonds pay coupons every six months and par value at maturity. The quoted coupon rate is annualized. That is if the quoted coupon rate is c and bond maturity is time T then for each 1 of par value the bond cash flows are c 2 c 2 c 2 1 c 2 ---------T ------ years 1 year years T years If the par value is N then the bond cash flows are Nc 2 Nc 2 Nc 2 N 1 c 2 r--------------- ------- ----------------- years 1 year years T years . Treasury Notes and Bonds Institutionally speaking . Treasury notes and bonds form a basis for the bond markets. The Treasury auctions new 2- 3- 5- 7-year notes monthly and 10-year notes and 30-year bonds quarterly as needed. See http offices domestic-finance debt-management auctions for a schedule. Non-competitive bidders just submit par amounts maximum 5 million and are filled first. Competitive bidders submit yields and par amounts and are filled from lowest yield to the stop yield. The coupon on the bond an even eighth of a percent is set to make the bond price close to par value at the stop yield. All bidders pay this price. See for example http fi FIFrameset page FISearchTreasury for a listing of outstanding Treasuries. Coupon Bonds and Zeroes 2 Debt Instruments and Markets Professor Carpenter Class Problem The current long bond the newly issued 30-year Treasury bond is the 3 7 8 s of August 15 2040. What are the cash flows of 1 000 000 par this bond Dates

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