# How do I define the “Coupon” within the function FinancialBond with a time-varying coupon

Is it possible using FinancialBond function to calculate the yield of a bond paying a gradual coupon ?

An example :

A bond with maturity of 7 years pays 4.125% the first 3 years, then 6% the next two and finally 7.75% the last two. The actual price of the bond is 102.35% and it is redeemed at par.

I know the answer using TimeValue and Cashflow functions. It is 5.14601% But I want to know if it is possible to calculate it straight from the FinancialBond function.

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It will be helpful if you register your account. Right now you have three different ones, with your reputation points fragmented across them. – Verbeia Apr 20 '12 at 9:25
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Please also stop posting clarifications to your question as "answers". – Verbeia Apr 23 '12 at 21:58

• The coupon may be specified as a single rate or a time-dependent payment function.

So, you should use

"Coupon" -> (Piecewise[{{.04125, #1 < 3}, {.06, 3 <= #1 < 5}, {.0775, 5 <= #1 < 7}}] &)


For example,

FinancialBond[{"FaceValue"->100,
"Coupon" -> (Piecewise[{{.04125, #1 < 3}, {.06, 3 <= #1 < 5}, {.0775, 5 <= #1 < 7}}] &),
"Maturity"->5},{"InterestRate"->r,"Settlement"->0}]


outputs

(* 100/(1+r)^5+(0.00125 (224.+375. r+345. r^2+165. r^3+33. r^4))/(1.+r)^5 *)

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This is not what I need. I'm not talking about an interest specification, but about a coupon changing over time. How do I define the time-dependent coupon ? As a list, it should be {.04125,.04125,.04125,.06,.06,.0775,.0775}. How get I such a list in "Coupon" ->... The purpose is to calculate the yield of such a bond using FindRoot[...] where within the function FinancialBond, the "InterestRate"->r (unknown) and the FindRoot equals 1.0425 or 1042.5 if I start with a FaceValue of 1,000. That's my problem. – Jean-Pierre Avermaete Apr 18 '12 at 20:46
Not sure I understand. Can you give an example of the calculation, but with a constant coupon? – Eli Lansey Apr 18 '12 at 20:51
FindRoot[FinancialBond[{"FaceValue" -> 100, "Coupon" -> Piecewise[{{.04125, #1 <= 3}, {.06, 3 < #1 <= 5}, {.0775, 5 < #1 <= 7}}] &, "Maturity" -> 7}, {"InterestRate" -> r, "Settlement" -> 0}] == 104.25, {r, 0.05}] – Jean-Pierre Avermaete Apr 18 '12 at 21:16
Sorry, I post it to quickly. When I try to solve the function sent before, this is the error message I get : FindRoot::nlnum: "The function value \!({(-104.25\) + FinancialBond[{\"FaceValue\" -> 100., \"Coupon\" -> Piecewise[{<<3>>}] &, \"Maturity\" -> 7.}, {\"InterestRate\" -> 0.05, \"Settlement\" -> 0.}]}\) is not a list of numbers with dimensions {1} at {r} = {0.05}." and nothing happens. When I use your Piecewise solution and give the appropriate yield, the function doesn't work either. – Jean-Pierre Avermaete Apr 18 '12 at 21:19
Just to keep things simple. The issue here is that the code: FinancialBond[{"FaceValue" -> 100, "Coupon" -> Piecewise[{{.04125, #1 <= 3}, {.06, 3 < #1 <= 5}, {.0775, 5 < #1 <= 7}}] &, "Maturity" -> 7}, InterestRate" -> r, "Settlement" -> 0}] Does not evaluate. FindRoot doesn't have anything to do with this. – Searke Apr 18 '12 at 21:30

Thanks to Sean Clarke from the Support department of Mathematica, I've got my solution. The way to solve such problem is to define the Coupon as a function. It becomes :

In[3]:= FindRoot[
FinancialBond[{"FaceValue" -> 1,
"Coupon" ->
Function[t,
Which[t <= 3, .04125, 4 <= t <= 5, .06, 6 <= t <= 7, .0775]],
"Maturity" -> 7}, {"InterestRate" -> r, "Settlement" -> 0}] ==
1.0235, {r, .05}]

Out[3]= {r -> 0.0514601}


I've tried other kind of gradual coupon bonds and this approach works perfectly. Thanks everybody for the replies.

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This is basically the same as my answer, just using Which rather than Piecewise. Also, I can't seem to get this to run as typed here. – Eli Lansey Apr 19 '12 at 22:34
@EliLansey, ... and your answer with Piecewise is about 10x faster. – kglr Apr 20 '12 at 0:07
kguler & Eli Lansey, I've tried once again your approach, but it doesn't work. I still get the same error message I mentioned before. How can you say that it's about ten times faster when it doesn't work ? Can you send me the exact formulation so I can test it ? – Jean-Pierre Avermaete Apr 20 '12 at 8:05
@Jean-PierreAvermaete What exactly is the error message you get? Are you doing a cut-and-paste on the code, or re-typing it? – Eli Lansey Apr 20 '12 at 14:45
@Jean-PierreAvermaete, for Which versus Piecewise you can try FindRoot[FinancialBond[{"FaceValue" -> 1, "Coupon" -> (Piecewise[{{0.04125, # <= 3}, {0.06, 4 <= # <= 5}, {0.0775, 6 <= # <= 7}}] &), "Maturity" -> 7}, {"InterestRate" -> r, "Settlement" -> 0}] == 1.0235, {r, 0.05}]//Timing and FindRoot[FinancialBond[{"FaceValue" -> 1, "Coupon" -> Function[t, Which[t <= 3, .04125, 4 <= t <= 5, .06, 6 <= t <= 7, .0775]], "Maturity" -> 7}, {"InterestRate" -> r, "Settlement" -> 0}] == 1.0235, {r, .05}] //Timing. – kglr Apr 21 '12 at 6:45

## protected by R. M.♦Apr 23 '12 at 21:57

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