Fixed Income

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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

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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 this fact that we are now facing a public debt crisis both in US and Europe. Indeed, the following graph points how after 2008 the trend of public debt steepened:

We are now relying more and more on indicators that characterize the bond market and that could provide information about the health of the economy. First of all, the so-called spread: the difference between the interest rates provided by two different

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bonds. The most widely used in Europe is definitely the spread against the German Bond: in difficult times this spread booms underlining the tension in the market. Another important indicator is the CDS (Credit Default Swap) spread, also related to the bond market. A CDS can be seen as a sort of insurance against a particular bond: in the period of crisis this indicator booms highlighting that in order to buy an insurance against the default of a given bond costs more.

Source: BIS

You can easily appreciate how strong the correlation between CDS spreads and Deficits is, and how much it costs to hedge against the default of Greece. However, we also have to point out that it is possible to buy a CDS without owning a bond: this is a naked CDS and is an explicit bet on the default of a country. This specific feature of CDS makes these instruments more sensitive to market‟s moods than common bond rates (which are stickier). All in all, the bond market is a very „populated‟ one, much more than the stock market. Hence, usually Bid-Ask spreads are very narrow due to high competitions among dealers (bond secondary markets are normally OTC) and arbitrage opportunities are normally exploited rapidly. However, on 7 January 1991 it seemed that there was room to make profits by replicating the 8¼ May 00-05 bond (8.25% coupon rate, callable from May 2000 until May 2005). III TWO SYNTHETIC BONDS  BUILD THE TWO SYNTHETIC BONDS It is possible to create two synthetic bonds, useful to exploit this arbitrage opportunity: - We can create a bond with the same cash...
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