Treasury Bond Futures Lecture

Treasury Bond Futures Lecture - Debt Instruments and...

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Debt Instruments and Markets Professor Carpenter Treasury Bond Futures 1 Treasury Bond Futures Basic Futures Contract Futures vs. Forward Delivery Options Underlying asset, marking-to-market, convergence to cash, conversion factor, cheapest-to-deliver, wildcard option, timing option, end-of- month option, implied repo rate, net basis Concepts and Buzzwords Reading Veronesi, Chapters 6 and 11 Tuckman, Chapter 14
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Debt Instruments and Markets Professor Carpenter Treasury Bond Futures 2 Basic Futures Contract In a basic futures contract without delivery options, the buyer agrees to take delivery of an underlying asset from the seller at a specified expiration date T . Associated with the contract is the futures price, G ( t ), which varies in equilibrium with time and market conditions. On the expiration date, the buyer pays the seller G ( T ) for the underlying asset. Marking to Market and Contract Value Each day prior to the expiration date, the long and short positions are marked to market: The buyer gets G ( t ) - G ( t - 1 day). The seller gets -( G ( t ) - G ( t - 1 day)). It costs nothing to get into or out of a futures contract, ignoring transaction costs. Therefore, in equilibrium, the futures price on any day is set to make the present value of all contract cash flows equal to zero.
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Debt Instruments and Markets Professor Carpenter Treasury Bond Futures 3 Marking to Market... Consider buying the contract at any time t and selling it after just one day. It essentially costs nothing to buy and sell the contract, so the payoff from this strategy is just the profit or loss from the marking to market: G ( t +1 day)- G ( t ). G ( t + 1 day) is random. G ( t ) is set today to make the market value of the next day’s random payoff G ( t +1 day)- G ( t ) equal to zero. Marking to Market... The market value of the random mark-to-market, G ( t + 1 day)- G ( t ), is the cost of replicating that payoff. We can represent that cost in the usual way as its discounted expected value under the risk-neutral probability distribution. To make this market value zero, today’s futures price must be the expected value of tomorrow’s futures price under the risk-neutral probability distribution: E t { t d t +1 day [ G ( t + 1 day)- G ( t )]}=0 => G ( t ) = E t { G ( t + 1 day)}.
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Debt Instruments and Markets Professor Carpenter Treasury Bond Futures 4 Convergence to Cash Consider entering the futures contract the instant before it expires. The long position would instantly pay the futures price and receive the underlying asset. The payoff would be V ( T )- G ( T ), where V ( T ) is the spot price of the underlying on the expiration date. In the absence of arbitrage, since it costs nothing to enter into either side of the contract, the (known) payoff must be zero: G ( T )= V ( T ).
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