Fixed Income
Case IV: Arbitrage in the Government Bond Market
Fixed income management (EBC4058)
Tutor: Micheal Viehs Coordinator: Thomas Post Group C: de Vivo Paolo 6057152 Bing-Jun Zhu 6030493 Honglei Zhao 6051963 04/03/2013
INDEX
I INTRODUCTION II BOND MARKET – A snapshot III TWO SYNTHETIC BONDS BUILD THE TWO SYNTHETIC BONDS PRICE OF THE SYNTHETIC BONDS IV HOW TO EXPLOIT THE ARBITRAGE OPPORTUNITY SPECULATING ON POSSIBLE REASONS V THE ADVANTAGES OF CALLABLE BONDS VI CONCLUSIONS VII PROBLEM SET Derive the arbitrage-free short rate tree using the Black-DermanToy model Value the bond using the given yields Value the bond using the short rates Value callable bonds Value call option VIII REFERENCES IX APPENDIX
1
I INTRODUCTION In this case we are going to investigate further arbitrage opportunities among Government Bond (and Bond-related) market. From a theoretical standpoint, this market should be extremely efficient due to the extremely large number of contracts negotiated and the presence of several different players (from private people to hedge funds). However, as underlined by our case, on 7 January 1991 a particular bond (8.25 May 00-05) seemed to be underpriced, providing room for arbitrage opportunities. In this paper, we are going to analyze how to exploit this arbitrage opportunity by replication. First, we will focus briefly on the features of US bond market. Second, we will build two synthetic securities (through STRIPS and other negotiated bonds) and we will show how to make profit from this price misalignment. Finally, we will provide some further comments and explanations on callable bonds. II BOND MARKET – A snapshot Nowadays, government bond markets around the world are booming mainly due to the fact that the amount of public debt is huge. Indeed, the 2008 crisis underlined private debt was too high and it was basically converted into public debt through bailouts and safety measures towards private companies. It is precisely due
Fixed income management (EBC4058)
Tutor: Micheal Viehs Coordinator: Thomas Post Group C: de Vivo Paolo 6057152 Bing-Jun Zhu 6030493 Honglei Zhao 6051963 04/03/2013
INDEX
I INTRODUCTION II BOND MARKET – A snapshot III TWO SYNTHETIC BONDS BUILD THE TWO SYNTHETIC BONDS PRICE OF THE SYNTHETIC BONDS IV HOW TO EXPLOIT THE ARBITRAGE OPPORTUNITY SPECULATING ON POSSIBLE REASONS V THE ADVANTAGES OF CALLABLE BONDS VI CONCLUSIONS VII PROBLEM SET Derive the arbitrage-free short rate tree using the Black-DermanToy model Value the bond using the given yields Value the bond using the short rates Value callable bonds Value call option VIII REFERENCES IX APPENDIX
1
I INTRODUCTION In this case we are going to investigate further arbitrage opportunities among Government Bond (and Bond-related) market. From a theoretical standpoint, this market should be extremely efficient due to the extremely large number of contracts negotiated and the presence of several different players (from private people to hedge funds). However, as underlined by our case, on 7 January 1991 a particular bond (8.25 May 00-05) seemed to be underpriced, providing room for arbitrage opportunities. In this paper, we are going to analyze how to exploit this arbitrage opportunity by replication. First, we will focus briefly on the features of US bond market. Second, we will build two synthetic securities (through STRIPS and other negotiated bonds) and we will show how to make profit from this price misalignment. Finally, we will provide some further comments and explanations on callable bonds. II BOND MARKET – A snapshot Nowadays, government bond markets around the world are booming mainly due to the fact that the amount of public debt is huge. Indeed, the 2008 crisis underlined private debt was too high and it was basically converted into public debt through bailouts and safety measures towards private companies. It is precisely due