Math Is Fun Forum

coffeeking

Member

Registered: 2007-11-18

Posts: 44

Financial Mathematics

Well I have problem understanding this question as I don't even know where to start. Would appreciate if anyone could sheath some light on how to tackle this question or at least give some hint on where to start.

The Z Corporation issues a 10%, 20-year bond at a time when yields are 10%. The bond has a call provision that allows the corporation to force a bond holder to redeem his or her bond at face value plus 5%. After 5 years the corporation finds that exercise of this call provision is advantageous. What can you deduce about the yield at that time? (Assume one coupon payment per year.)

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Financial Mathematics

Hi coffeeking;

I found this:
http://74.125.95.132/search?q=cache%3A5 … l=en&gl=us

On page 8 is your problem.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

coffeeking

Member

Registered: 2007-11-18

Posts: 44

Re: Financial Mathematics

Hi bobbym thanks for the link. However after following through the working I end up having to solve a 15 degree polynomial:

Are there any easier method?

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Financial Mathematics

Hi coffeeking;

I haven't read the paper thoroughly but I would use some iterative form or newtons iteration to get the roots.
If I remember was it a series that generated that inequality? Do you need to solve them on a daily basis?

Last edited by bobbym (2009-08-09 18:51:40)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

coffeeking

Member

Registered: 2007-11-18

Posts: 44

Re: Financial Mathematics

The series that you are refering to is:

which can be simplified to:

using the formula for geometric series.

I am just doing some practices questions from my textbook on my own by the way.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Financial Mathematics

Hi coffeeking;

You did a nice job on the summation and the simplification.

I am just doing some practices questions from my textbook on my own by the way.

Post em, if their interesting or troublesome.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

George,Y

Member

Registered: 2006-03-12

Posts: 1,379

Re: Financial Mathematics

the yield r just need to satisfy
pv(r)=10/(1+r)+10/(1+r)²+...+10/(1+r)[sup]14[/sup]+110/(1+r)[sup]15[/sup]>105

note pv is a decreasing function, so you just make sure r>r0 where r0 satisfies pv(r0)=105

And r0 can be solved by a functio like IRR. You just need a financial calculater to do the job, or present value tables, coffeeeking.

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X'(y-Xβ)=0

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Financial Mathematics

Hi coffeeking;

George has a point. Go here for more info:

http://en.wikipedia.org/wiki/Internal_rate_of_return

But you still have to use either iteration or a financial calculator to get the answer. They are recommending the secant method for the root.

Last edited by bobbym (2009-08-22 02:53:57)

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Identity

Member

Registered: 2007-04-18

Posts: 934

Re: Financial Mathematics

You could also graph it if you use a graphics calculator and find zeros from that.

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Financial Mathematics

Hi identity;

That is pretty much how I solved it in post #4. I used the locus to locate the root and then used several iterative forms to zero in.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.