HOW TO SOLVE e^2R= 0.90506?

[Shazam023]

'm doing Swaps valuation and discounting coupon pmts. with spot rates.
so there's an example in Hull which asks for final pmt's spot rate.

so m not able to solve this e^2R=0.90506 for R...
can someone help?

R shud be 4.99%

and is there any other way to calculate R other thn e^x.
earlier i was using 1/(1+r)^n but through that m getting 5.11%

 

[Deepak Chitnis]

Hi @Shazam023, e^2R=0.90506, you can solve it using LN , like 2R=LN(0.90506). as 2R=-0.09975. R=-0.09975/2=-0.04988=4.99%. Please ignore the signs. Hope that helps. Thank you!

 

[Shazam023]

Hi @Shazam023, e^2R=0.90506, you can solve it using LN , like 2R=LN(0.90506). as 2R=-0.09975. R=-0.09975/2=-0.04988=4.99%. Please ignore the signs. Hope that helps. Thank you!

@Deepak Chitnis thnkx man.... this is so simple..

can u explain that is there any difference in these 2 terms:

e^(0.02)(3/12) & 1/(1+0.02)^3/12

i m using the second term for discounting purposes but in books the "e^x" term is used and my answers r just lil bit different.. 2~3 decimal point difference....

 

[Deepak Chitnis]

Hi @Shazam023, first term is used when the compound frequency is continuice and secon term when compound frequency is discret (annual, semi annual etc.) hope that helps. Thank you

 

[Dr. Jayanthi Sankaran]

Hi @Shazam023,

e^(-0.02)*(3/12) = 0.995012 and 1/(1 + 0.02)^3/12 = 0.995062. The former uses continuous compounding and the latter uses discrete compounding (annual, semi-annual compounding etc.). Hull always uses continuous compounding in his interest rate calculations. However, Tuckman and some others use semi-annual discrete compounding. In Japan they use discrete annual compounding.

That is why in the Chapter on Swaps (which can be thought of as a long position in a floating rate bond with a short position in a fixed rate bond and vice-versa), Hull uses continuous compounding.

However, it must be clarified here that while Hull computes the coupon cash flows using semi-annual discrete compounding, he uses continuous compounding to discount those cash flows. Hope that helps!

Thanks!

 

[Shazam023]

Thnkx to both of u...

Will there be any significant difference if I use first instead of second??

 

[Dr. Jayanthi Sankaran]

Hopefully, it will be specified as to whether to use continuous compounding or discrete compounding to discount the cash flows

Thanks!
Jayanthi