# fixed for floating currency swap

#88311 90 days ago the exchange rate for the Canadian dollar (C\$) was 0.83 and the term structure was: 180 days 360 days LIBOR 5.6% 6% CDN 4.8% 5.4%. A swap was initiated with payments of 5.3% fixed in C and floating rate payments in USD on a notional principal of USD 1 million with semiannual payments. 90 days have passed, the exchange rate for C\$ is \$0.84 and the yield curve is: 90 days 270 days LIBOR 5.2% 5.6% CDN 4.8% 5.4% What is the value of the swap to the floating-rate payer? A) −\$2,708. B) \$3,472. C) \$10,125. The correct answer was C) \$10,125 ----- How do I calculate the PV 1 USD, which is the floating outflow. It’s given as (1.028 / 1.013), but i dont understnad the logic behind it. why is it (1.028 / 1.013) and not (.028)(Z90) + (1.028)(Z270)?

1. floating bond resets to par on payment date. and the payment date is an anniversary (kind of) 90 days later when the LIBOR resets. So 1.028 (which was the coupon you received on the fixed + principal 1\$) needs to be discounted for 90 days … time period left to elapse. 0…90…180 Initially …1.028 Now …90…1.028 xxxxxxxxxxx

thanks cpk. really appreciate u answering some of the harder questions i’ve asked.

What am I doing wrong I get \$14,756 For the floating US 1.028/1.013 = \$27,640 For the Canadian .0265/(1.012) + 1.0265/(1.0405) = 1.0127 1.0127 is paid on (1000000/.83) dollars which is then multiplies by .84 to get the current amount at todays rates.

Actually you multiply by .83 and divide by .84.

sebrock Wrote: ------------------------------------------------------- > What am I doing wrong I get \$14,756 > > For the floating US > > 1.028/1.013 = \$27,640 > > For the Canadian > > .0265/(1.012) + 1.0265/(1.0405) = 1.0127 > > 1.0127 is paid on (1000000/.83) dollars which is > then multiplies by .84 to get the current amount > at todays rates. Canadian is floating, you only need the PMT based on beginning period of labor + principal discounted until next reset date.

(USD .85069404)(CAD 1,204,819) = USD 1,024,932 USD 1,024,932 - USD 1,014,807 = \$10,125

i have no idea how to do this, gonna study up on it tomorrow.

Thanks, had the math right. I messed up a parens in excel. It was driving me nuts because I do know how to do these ok. I’ll go through it step by step for those that want a review. First is the US floating side which is based on the previous LIBOR coupon on 5.6%. Because it is a six month payment with 90 days remaining the value is as follows: 1.028 / 1.013 = 1.014807 this is what your interest and principal is worth today if you were exchanging cash flows. So multiplied by the \$1,000,000 notional, a payment of \$1,014,807 is has to be made. Next comes the Canadian fixed piece. Your original fixed payment of 5.3% for 1,000,000 notional when the currency was .83/1 C\$. We get the value of the swap by treating it as a one year bond with two coupon payments, so the formula is as follows: .026 / (1 +( 4.8% (90/360))) + 1.026 / (1+ (5.4% (270/360))) = 1.012731 Now comes the currency part. Remember that the 1.012731 is paid on the 1,000,000 you exchanged at .83/1 \$C so it’s \$1,000,000 / .83 = \$C 1,204,819 plus the interest received on this amount \$1,204,819 * 1.012731 = \$C 1,220,158 which now you have to convert back to dollars in order to swap payments so \$1,220,158 * .84 (the current exchange rate) leaves you with \$1,024,932. So you receive \$1,024,932 from the fixed Canadian swap and pay \$1,014,807 for the US floating payment which leaves you a profit of \$10,125.