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trc
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Joined: April 4th, 2002, 2:28 pm

### Methods of yield to maturity calculation

There seem to be several methods to calculate the yield to maturity of a bond but it is difficult (and I failed to) find the definition of these standards.

Let's review the situation: once the size and timing of the bond cashflows are fixed (via bond base data, holiday calendar, business day convention and day count convention) the manner of discounting the cashflows needs to be chosen to arrive at the dirty price of the bond given the yield to maturity y.
This then defines the function yield y --> dirty_price(y).

The naive assumption now is that the yield to maturity as a function of the dirty price, dirty price dp --> yield(dp), is simply the inverse of the former function. Unfortunately this is not exactly true as there seem to be various methods of yield computation which apply special rules in addition to  function inversion.

This comprises the "yield computation method" which consists of
(a) specifying the manner of cashflow discounting to arrive at the dirty price
(b) special rules to be applied in addition to function inversion  to compute the yield y from the dirty price dp.

Whenever you do a search for such methods you end up with the following:
(A) cashflow discounting is geometric with the same frequency as the bond coupon (discount factors (1+y/m)^(-t), where m is the number of coupons per year
and t is time to cashflow computed as the number of coupon periods, generally fractional).
(B) The yield is computed from the dirty price by straightforward inversion of the function yield y --> dirty price dp=dp(y).

This seems to be the yield computation method "ICMA" and is the only one for which I could find something approaching a definition by the organisation responsible for the standard. But there also seem to be other methods. For example a handbook much in use in Germany cites the following yield
computation methods:
"German", "ISMA", "US Treasury", "SIA", "Japanese"
without giving enough detail to amount to a precise definition.

To give you an idea as to what can be involved I encountered a rumour that the following yield computation method exists:
(I) to compute the dirty price from a yield you discount all cashflows continuously (i.e. exponentially) except the first one, where you use simple discounting.
(II) to compute the yield from the dirty price you invert the above function yield --> dirty_price but then convert the yield y so computed to the equivalent rate of interest compounded continuously.

Note that this is rather bizarre : to convert a rate y of interest into an equivalent rate using a different manner of compounding you must especially know the manner of compounding used with the rate y which in the case above is the bizarre (I). Please don't ask me where I got this from as in general I can't find any precise definitions.

My question therefore is the following: what are the authoritative sources on these yield computation methods, where are the precise definitions?