Fixed Income
MF 728 Fixed Income Securities M.S. in Mathematical Finance Boston University School of Management Bond Issue at RLC & Co. Rindisoand Co. (RLC) is a Boston-based private bank which needs to borrow in order to nance the renovation of its plush downtown oces. To this end, the partners are considering the possibility of issuing a bond with the following characteristics: { Face Value: N { Maturity: 10 Years. { Coupon rate: C% per year. { Coupon frequency: every 6 months.
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MF 728 Fixed Income Securities M.S. in Mathematical Finance Boston University School of Management Bond Issue at RLC & Co. Rindisoand Co. (RLC) is a Boston-based private bank which needs to borrow in order to nance the renovation of its plush downtown oces. To this end, the partners are considering the possibility of issuing a bond with the following characteristics: { Face Value: N { Maturity: 10 Years. { Coupon rate: C% per year. { Coupon frequency: every 6 months. In order to attract investors, the partners want to grant the bond holders the possi- bility of putting the bond in 5 years at a clean price of $K per dollar of face value. Since you are the best of their quantitative analysts (BU-MF trained of course), the partners have come to you for an in-depth study of the proposed bond issue. 1. Analysis of the bond issue (a) Show that the price of the bond is equal to that of a portfolio which contains i) a long position in an option-free but otherwise identical coupon bond, and ii) a long position in a 5Y European put option written on that option-free coupon bond. What is the strike price of that put option? What is the value of the putable bond at the put date? Assume that K = 1 and consider two option-free bonds both of which have annual coupon rate C paid in two semiannual installments and assume that the rst bond has a maturity of 5 years while the second bond has a maturity of 10 years. (b) Show that the price of RLC’s bond is always higher than the maximum of the prices of these two bonds. 1(c) Explain why the price of the putable bond approaches the price of the shorter straight bond as interest rates increase and the price of the longer straight bond as interest rates decrease. What impact does this have on the duration and the convexity of the bond? Briey explain. The yield to put on a putable bond is the yield oered by the bond under the assumption that the put option will denitely be exercised. In contrast, the yield to maturity on a putable bond is…
MF 728 Fixed Income Securities M.S. in Mathematical Finance Boston University School of Management Bond Issue at RLC & Co. Rindisoand Co. (RLC) is a Boston-based private bank which needs to borrow in order to nance the renovation of its plush downtown oces. To this end, the partners are considering the possibility of issuing a bond with the following characteristics: { Face Value: N { Maturity: 10 Years. { Coupon rate: C% per year. { Coupon frequency: every 6 months. In order to attract investors, the partners want to grant the bond holders the possi- bility of putting the bond in 5 years at a clean price of $K per dollar of face value. Since you are the best of their quantitative analysts (BU-MF trained of course), the partners have come to you for an in-depth study of the proposed bond issue. 1. Analysis of the bond issue (a) Show that the price of the bond is equal to that of a portfolio which contains i) a long position in an option-free but otherwise identical coupon bond, and ii) a long position in a 5Y European put option written on that option-free coupon bond. What is the strike price of that put option? What is the value of the putable bond at the put date? Assume that K = 1 and consider two option-free bonds both of which have annual coupon rate C paid in two semiannual installments and assume that the rst bond has a maturity of 5 years while the second bond has a maturity of 10 years. (b) Show that the price of RLC’s bond is always higher than the maximum of the prices of these two bonds. 1(c) Explain why the price of the putable bond approaches the price of the shorter straight bond as interest rates increase and the price of the longer straight bond as interest rates decrease. What impact does this have on the duration and the convexity of the bond? Briey explain. The yield to put on a putable bond is the yield oered by the bond under the assumption that the put option will denitely be exercised. In contrast, the yield to maturity on a putable bond is…
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