Par yield and Poisson distribution: Difference between pages

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imported>Doug Williamson
(Colour change of example headers)
 
imported>Doug Williamson
(Add 'with no upper limit' to differentiate from binomial distribution.)
 
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Today’s market yield on a coupon paying bond trading at par and redeemable at par
<i>Statistics</i>.
= the fixed coupon rate payable on such a ‘par bond’.


A probability model used where discrete events occur in a continuum.


<span style="color:#4B0082">'''Example'''</span>
For example, the number of phone calls received in a given time period.


The par yield for the maturity 0-3 periods is 1.90% per period.
This means that a deposit of £1,000,000 at Time 0 periods on these terms would return:
*Interest at a rate of 1.90% per period on the original £1,000,000, at Times 1, 2 and 3 periods, and
*The principal of £1,000,000 at Time 3 periods
The interest payments will be £1,000,000 x 0.019 = £19,000 per period
The total repaid at Time 3 periods will be: principal £1,000,000 + £19,000 interest = £1,019,000.
An application of par yields is the pricing of new coupon paying bonds.
The par yield is known as the Par rate, Swap rate or Swap yield.
'''Conversion'''
If we know the par yield, we can calculate both the [[zero coupon yield]] and the [[forward yield]] for the same maturities and risk class.


The Poisson distribution can be a useful model for processes where:
#Continuous observation is needed, rather than a number of independent trials.
#The random variable takes a positive whole number (integer) value, with no upper limit.
#The expected number of occurrences is known or can be estimated, and
#Primary interest is in the number of times an event occurs within a particular period.




== See also ==
== See also ==
* [[Bond]]
* [[Discrete random variable]]
* [[Bootstrap]]
* [[Binomial distribution]]
* [[Coupon bond]]
* [[Frequency distribution]]
* [[Forward yield]]
* [[Probability]]
* [[Market yield]]
* [[Par]]
* [[Swap spread]]
* [[Yield curve]]
* [[Zero coupon yield]]
* [[Flat yield curve]]
* [[Rising yield curve]]
* [[Falling yield curve]]
* [[Positive yield curve]]
* [[Negative yield curve]]

Revision as of 11:06, 7 August 2014

Statistics.

A probability model used where discrete events occur in a continuum.

For example, the number of phone calls received in a given time period.


The Poisson distribution can be a useful model for processes where:

  1. Continuous observation is needed, rather than a number of independent trials.
  2. The random variable takes a positive whole number (integer) value, with no upper limit.
  3. The expected number of occurrences is known or can be estimated, and
  4. Primary interest is in the number of times an event occurs within a particular period.


See also