I am looking for what I believe is called the ?Cost of Carry? price
and/or yield formula for TIPS
(http://www.investopedia.com/terms/t/tips.asp). The Cost of Carry is
an increase or decrease of a buying/selling price due to the actual
trade settling some time in the future.
Specifically, I need the mathematical formula that generates the
results given below.
Here is an example of the available data of a TIP called TII 3
07/15/12. I want to know how given the following data, I can achieve
the price and yield results for this and all other TIPS.
Available Data:
Issue Name: TII 3 07/15/12
CUSIP: 912828AF7
These calculations occur on: 8/25/04
Starting price: 109.84449
Starting yield: 1.663088
Maturity Date: 7/15/12
Issue Date: 7/15/02
1st Coupon Date: 1/15/03
Issue/Coupon Rate: 3
2 Coupons per year
This is data I want to know how to generate, given any rate or date:
Price and yield answers given a Cost of Carry Rate of 1:
On 8/26 the Cost of Carry price is 109.828125, yield: 1.66436
8/27- price: 109.8125, yield: 1.66641
8/28- price: 109.796875, yield: 1.66813
8/29- price: 109.78125, yield: 1.66986
Price and yield answers given a Cost of Carry Rate of 2:
On 8/26 the Cost of Carry price is 109.828125, yield: 1.66436
8/27- price: 109.8203125, yield: 1.66563
8/28- price: 109.8046875, yield: 1.66794
8/29- price: 109.7890625, yield: 1.66831
I can provide more data for this or other TIPS upon request.
The formula needs to give results accurate to the thousandth place (.000).
How about this.. http://theponytail.net/DOL/DOLnode33.htm
I have a feeling all the formulae are in
http://theponytail.net/DOL/DOLnode25.htm somewhere. (It seems nearly
every link has a formula.)
I think/hope that you'll be able to fill in the variables appropriately.
alltheweb search: "Cost of carry"
I am not a Google Answers Researcher.
I noticed the same thing with the price difference being off on the
first day with the rate of 2. It gives me comfort to know I'm not the
only one working on this problem.
I will post more data on 2 totally difference TIPs by Monday evening
at the latest. Unfortunately, you'll again see patterns that seem to
emerge, and then break for no apparent reason. Like the 1st and 2nd
day are off by the same difference, and then the third day is way off,
etc...
I certainly appriciate the help you've offered so far. I will look
into the links you have posted in futher detail and post any relevant
knowledge that might help both of us.
Thank you!
Maybe buy the author's book? http://www.espenhaug.com/books.html
The Complete Guide to Option Pricing Formulas
From http://home.online.no/~espehaug/BlackScholes.html
Since you are referring to Black Scholes,
http://www.riskglossary.com/articles/black_scholes_1973.htm gives the
formula. (note the related books... Espen Haug is listed.)
http://en.wikipedia.org/wiki/Black-Scholes gives more detail, points
to http://en.wikipedia.org/wiki/Binomial_options_model for American
Options..
Still isn't what you're looking for, I guess, but I'm hoping this helps a bit.
Ah! Hmm.. ok. well, I think I understand a bit better the question.
Still don't think I have the answer, but I believe I'm getting closer.
Please understand I'm doing this for free. The question seems
intriguing. I'm just surprised Mathtalk-ga isn't on this as well... \documentclass[11pt,plainpaper]{article}::
File Format: Microsoft Word - View as HTMLTo summarize, when the index futures satisfies the cost of carry formula, the Stoll P-C parity condition and the P-C-F parity conditions are identical.
http://privatewww.essex.ac.uk/~scher/20Folder/Nov30P-C-Farbf.docHOME |
Sorry, I didn't see any formula on those pages that results in the
answers given above.
You are in the correct problem space, but we need to go a little
deeper. These pages seem to contain specific data for specific TIPS,
but no general formulas. I am hoping to find / derive the formula for
calculating Cost of Carry on any TIP given the relevant "Available
Data" as above.
I'm looking for something like (obviously not the correct formula):
New Cost of Carry Price = originalPrice + (daysToMaturity/CouponRate)
* daysFromLastCoupon/daysToNextCoupon ^ (CostOfCarryRate /
daysCarried)
I am programming a financial calculator in the spirit of:
http://home.online.no/~espehaug/BlackScholes.html and need this
formula to give accurate results. I know the formula exists because
I've seen this calculation performed in other applications given the
relevant "Available Data". Regretfully those other applications are
totally closed off from decompiling / documentation / support / etc...
so I cannot glean any information from them, other than the correct
answers given a set of data.
Hopefully the appropriate formula is on an information page just a few
clicks away from links you found, but I couldn't find it, if it is.
You seem to be in the right area, though.
I think it's actually released as a document from the federal
government... http://www.publicdebt.treas.gov/of/ofinflin.htm
I'd like to be able to help you, although I see way different numbers
in the ftp://ftp.publicdebt.treas.gov/of/of082004cpi.pdf than those
you have provided.
I think I'm in the wrong class of numerics.
If this isn't helping at all, I apologize.
Here is some additional data from a different TIP
Available Data:
Issue Name: TII 4 1/4 01/15/10
CUSIP: 9128275W8
These calculations occur on: 8/25/04
Starting price: 115.73452
Starting yield: 1.223574
Maturity Date: 01/15/10
Issue Date: 01/18/00
1st Coupon Date: 7/15/00
Issue/Coupon Rate: 4.25
2 Coupons per year
This is data I want to know how to generate, given any rate or date:
Price and yield answers given a Cost of Carry Rate of 1:
8/26- price: 115.71875, yield: 1.22569
8/27- price: 115.6953125, yield: 1.22799
8/28- price: 115.671875, yield: 1.23011
8/29- price: 115.65625, yield: 1.23242
Price and yield answers given a Cost of Carry Rate of 2:
8/26- price: 115.71875, yield: 1.22512
8/27- price: 115.703125, yield: 1.22685
8/28- price: 115.6875, yield: 1.22840
8/29- price: 115.6640625, yield: 1.23013
Why is the first date SO different in calculations from every other date?
I hope this looks right
price difference yield difference
109.828125 1.664360
109.812500 -0.015625 1.666410 0.002050
109.796875 -0.015625 1.668130 0.001720
109.781250 -0.015625 1.669860 0.001730
109.828125 1.664360
109.820313 -0.007813 1.665630 0.001270
109.804688 -0.015625 1.667940 0.002310
109.789063 -0.015625 1.668310 0.000370
I see the price move predictably after the first day, but it's really
off for the Carry rate of 2. For a carry rate of 1, I could possibly
predict that the yield increase would otherwise continue to increase
at a rate of 0.000010.. for Carry rate of 2, I have to probably see
more data. If I copied correctly, there doesn't seem to be a logical
reason for your yield to vary as widely as it does per day.
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Cost of Carry Formula for TIPS