Sunday, May 7, 2017

how to derive yield curve from interest rate swap?


According to some textbooks, to derive the yield curve, quote



  • overnight to 1 week: rates from interbank money market deposit,

  • 1 month to 1 year: LIBOR;

  • 1 year to 7 years: Interest Rate Swap;


  • 7 years above: government bond.


I'm a bit lost here: how can an IRS rate be used to derive yield curve?


Yield rate is the discount rate, if yield(5years)=4.1% , it means the NPV of 1 dollar 5 years later is NPV(1dollar,5years)=1/[(1+4.1%)5]=0.818.


While interest rate swap is a contract among to legs. Assume a 5 years' IRS contract is



  • leg A pays fixed rate to B @ 8.5%, while A receives floating rate @ LIBOR +1.5%

  • leg B pays floating rate to A @ LIBOR +1.5%, B receives fixed rate@ 8.5%.


, how could this swap contract help deriving the 5 years' yield rate?




Answer



You should take a look at the example from Hull's book.


Assume that the 6-month, 12-month, 18-month zero rates are 4%, 4.5%, and 4.8%, respectively.


Suppose we know that the 2-year swap rate is 5%, which implies that a 2-year bond with a semiannual coupon of 5% per annum sells for par: 2.5e0.040.5+2.5e0.0451.0+2.5e0.0481.5+102.5e2R=100. Solving for R above gives a 2-year zero rate R of 4.953%. We can keep going to compute the 3-year zero rates, etc.


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