If I want the fair price of a bond with coupon interval twice per year with interest rate $i$ p.a., I use "CouponInterval"->1/2. However, the InterestRate should be the effective, or nominal interest rate?
Thank you for help.
2 Answers
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It's all in the Documentation Center:
By convention, yield to maturity and coupon specifications are assumed to be nominal with a compounding interval equal to the coupon payment interval. By using the EffectiveInterest function or a functional interest rate specification, any desired compounding can be achieved.
(...)
FinancialBond takes a nominal yield and assumes a compounding equal to the coupon frequency. However, it may be desirable to use a different compounding frequency. EffectiveInterest can be used to find a rate that gives the correct effective discounting after being compounded at the coupon frequency:
Solve[EffectiveInterest[r, 1/2] == EffectiveInterest[.05, 0], r]
{{r -> -4.05063}, {r -> 0.0506302}}
FinancialBond[{"FaceValue" -> 1000, "Coupon" -> .05, "Maturity" -> 10,
"CouponInterval" -> 1/2}, {"InterestRate" -> 0.0506302,
"Settlement" -> .2}]
(* ==> 995.103 *)
Hence my advice:
Do with Mathematica what your lecturer desires :)
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$\begingroup$ Thanks. I was searching on reference.wolfram.com/mathematica/ref/FinancialBond.html and couldn't find that detail $\endgroup$– DahnJun 3, 2014 at 18:01
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Through experimenting, I was able to realize my error and thus realize that the InterestRate is, in fact, nominal.
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$\begingroup$ Well, it wasn't exactly an error, but rather a nice little demonstration of the many possible ways how they get our money :) $\endgroup$– eldoJun 3, 2014 at 19:20