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Unformatted text preview: Chapter 8 Swaps Question 8.1. We frst solve For the present value oF the cost per two barrels: $22 1 . 06 + $23 ( 1 . 065 ) 2 = 41 . 033 . We then obtain the swap price per barrel by solving: x 1 . 06 + x ( 1 . 065 ) 2 = 41 . 033 x = 22 . 483 , which was to be shown. Question 8.2. a) We frst solve For the present value oF the cost per three barrels, based on the Forward prices: $20 1 . 06 + $21 ( 1 . 065 ) 2 + $22 ( 1 . 07 ) 3 = 55 . 3413 . We then obtain the swap price per barrel by solving: x 1 . 06 + x ( 1 . 065 ) 2 + x ( 1 . 07 ) 3 = 55 . 341 x = 20 . 9519 b) We frst solve For the present value oF the cost per two barrels (year 2 and year 3): $21 ( 1 . 065 ) 2 + $22 ( 1 . 07 ) 3 = 36 . 473 . We then obtain the swap price per barrel by solving: x ( 1 . 065 ) 2 + x ( 1 . 07 ) 3 = 36 . 473 x = 21 . 481 104 Chapter 8 Swaps Question 8.3. Since the dealer is paying fxed and receiving Foating, she generates the cashFows depicted in column 2. Suppose that the dealer enters into three short orward positions, one contract or each year o the active swap. Her payos are depicted in columns 3, and the aggregate net cash Fow position is in column 4. Year Net Swap Payment Short orwards Net Position 1 S 1 $20 . 9519 $20 S 1 0.9519 2 S 1 $20 . 9519 $21 S 1 + 0.0481 3 S 1 $20 . 9519 $22 S 1 + 1.0481 We need to discount the net positions to year zero. We have: PV (netCF) = . 9519 1 . 06 + . 0481 ( 1 . 065 ) 2 + 1 . 0481 ( 1 . 07 ) 3 = . Indeed, the present value o the net cash Fow is zero. Question 8.4. The air swap rate was determined to be $20.952. Thereore, compared to the orward curve price o $20 in one year, we are overpaying $0.952. In year two, this overpayment has increased to $0 . 952 1 . 070024 = 1 . 01866, where we used the appropriate orward rate to calculate the interest payment. In year two, we underpay by $0.048, so that our total accumulative underpayment is $0.97066. In year three, this overpayment has increased again to $0 . 97066 1 . 08007 = 1 . 048. However, in year three, we receive a fxed payment o 20.952, which underpays relative to the orward curve price o $22 by $22 $20 . 952 = 1 . 048. Thereore, our cumulative balance is indeed zero, which was to be shown. Question 8.5. Since the dealer is paying fxed and receiving Foating, she generates the cashFows depicted in column 2. Suppose that the dealer enters into three short orward positions, one contract or each year o the active swap. Her payos are depicted in columns 3, and the aggregate net position is summarized in column 4....
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This note was uploaded on 12/06/2011 for the course ECON 101 taught by Professor Adam during the Spring '06 term at Neumann.
 Spring '06
 Adam

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