Lecture_06

Lecture_06 - 6 Trading Strategies, Arbitrage Opportunities,...

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1 6 Trading Strategies, Arbitrage Opportunities, and Complete Markets A Motivation These are the basic concepts needed to develop the pricing and hedging methodology for fixed income securities and interest rate options. B Trading Strategies Intuitively, a trading strategy is a dynamic investment portfolio involving the traded zero- coupon bonds. Portfolio rebalancings can occur within the investment horizon and they are based on the information available at the time that the portfolio is rebalanced.
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2 EXAMPLE: A TRADING STRATEGY A trading strategy is a complete (state and time contingent) listing of the holdings of each traded security for each time and state in a tree. A trading strategy imposes no restrictions on these holdings.
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3 Figure 6.1: An Example of a Zero-coupon Bond Price Curve 2 1 0 1 976147 . 953877 . 1 978085 . 957211 . 937148 . 1 981169 . 962414 . 1 980392 . 961169 . 942322 . 923845 . ) 0 , 0 ( ) 1 , 0 ( ) 2 , 0 ( ) 3 , 0 ( ) 4 , 0 ( 1 980015 . 960529 . 1 982699 . 965127 . 947497 . 1 984222 . 967826 . time P P P P P =
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4 Figure 6.2: An Example of a Zero-coupon Bond Price Curve Evolution and a Trading Strategy (n 0 (t), n 4 (t), n 3 (t), n 2 (t)). 2 1 0 time (0,0,0,0) 1 976147 . 953877 . 1.042854 ) -.5962084 (0,0,0, 1 978085 . 957211 . 937148 . (0,0,0,0) 1.02 1 981169 . 962414 . 1.042854 1 980392 . 961169 . 942322 . 923845 . ) 0 , 0 ( P ) 1 , 0 ( P ) 2 , 0 ( P ) 3 , 0 ( P ) 4 , 0 ( P (0,0,0,0) 1 B(0) 1 980015 . 960529 . 1.037958 (0,0,3.5,0) 1 982699 . 965127 . 947497 . (0,0,0,0) 1.02 1 984222 . 967826 . 1.037958 = () ) 2 , 5 . 2 , 0 , 1 ( ) 0 ( n ), 0 ( n ), 0 ( n ), 0 ( n 2 3 4 0 = r(0) = 1.02 1.017606 1.022406
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5 At time 0, the holdings vector is: )) 0 ( 2 ), 0 ( 3 ), 0 ( 4 ), 0 ( 0 ( n n n n = ( -1, 0, 2.5, -2). ) 0 ( 0 n is the number of units of the money market account held at time 0. ) 0 ( 4
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This note was uploaded on 12/09/2008 for the course NBA 5550 taught by Professor Jarrow,robert during the Fall '08 term at Cornell.

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Lecture_06 - 6 Trading Strategies, Arbitrage Opportunities,...

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