M08_MCDO8122_01_ISM_C08

# M08_MCDO8122_01_ISM_C08 - Chapter 8 Swaps n Question 8.1 We...

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Chapter 8 Swaps n Question 8.1 We first solve for the present value of the cost per two barrels: 2 \$22 \$23 41.033. 1.06 (1.065) + = We then obtain the swap price per barrel by solving: 2 41.033 (1.065) 1.06 22.483, x x x + = = which was to be shown. n Question 8.2 1. We first solve for the present value of the cost per three barrels, based on the forward prices: 2 3 \$20 \$21 \$22 55.3413. 1.06 (1.065) (1.07) + + = Hence we could spend \$55.3413 today to receive 1 barrel in each of the next three years. We then obtain the swap price per barrel by solving: 2 3 55.3413 1.06 (1.065) (1.07) 20.9519 x x x x + + = = 2. We first solve for the present value of the cost per two barrels (Year 2 and Year 3): 2 3 \$21 \$22 36.473. (1.065) (1.07) + = Hence we could spend \$36.473 today and receive 1 barrel of oil in Year 2 and Year 3. We obtain the swap price per barrel by finding two equal payments we would make in Years 2 and 3 that have the same present value: 2 3 36.473 (1.065) (1.07) 21.481 x x x + = =

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94 McDonald • Fundamentals of Derivatives Markets n Question 8.3 Since the dealer is paying fixed and receiving floating, each year she has a cash flow \$20.9519. T S - She can hedge this risk by selling 1 barrel forward (i.e., short one forward) in each of the three years. Her payoffs from the swap, the short forward contracts, and the net are summarized in the following table: Year Net Swap Payment Short Forwards Net Position 1 1 \$20.9519 S - 1 \$20 S - - 0.9519 2 2 \$20.9519 S - 2 \$21 S - + 0.0481 3 3 \$20.9519 S - 3 \$22 S - + 1.0481 We need to discount the net cash flows to year zero. We have: 2 3 0.9519 0.0481 1.0481 PV(net CF) 0. 1.06 (1.065) (1.07) - = + + = Indeed, the present value of the net cash flow is zero. n Question 8.4 The fair swap rate was determined to be \$20.9519. Therefore, compared to the forward curve price of \$20 in one year, we are overpaying \$0.9519. In year two, with interest, this overpayment increases to \$0.9519 1.070024 \$1.01853, × = where we used the appropriate forward rate to calculate the interest payment. In year two, we underpay by \$0.0481, so that our total accumulative underpayment is \$1.01856 - \$0.0481 = \$0.97042. In year three, using the appropriate 1-year forward rate of 8.007%, this net overpayment increases to\$0.97046 1.08007 \$1.0481. × = However, in year three, we receive a fixed payment of 20.9519, which underpays relative to the forward curve price of \$22 by\$22 \$20.9519 \$1.0481. - = Therefore, our cumulative balance is indeed zero, which was to be shown. n
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M08_MCDO8122_01_ISM_C08 - Chapter 8 Swaps n Question 8.1 We...

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