Fixed Income Mathematics

ACCURACY REQUIREMENTS

You set the accuracy requirements for your approximation. This really means

that the job you are doing sets the requirements. Different jobs will have dif-

ferent requirements. For example, most financial mathematics approximation

jobs do not require particularly great precision. Making rockets to circle the

planet Jupiter will have great precision requirements. Determining these pre-

cision requirements might be the hardest part of the actual approximation job.

LEGAL REQUIREMENTS FOR ACCURACY

Sometimes the accuracy requirements are stated legally. For example, the

Municipal Securities Rulemaking Board (MSRB), one of the regulatory author-

ities for the municipal securities industry, requires that the yield equivalent of

the dollar price must be shown on the customer confirmation, accurate to

within .05% of yield, if the bond was traded at a dollar price. The MSRB has

devoted a whole section of a rule to accuracy requirements. You should always

make sure that any legal or regulatory requirements have been met in calcu-

lation of approximate numbers. Check with the rule publications, or your com-

pliance officer, for the requirements. A book like this is not a good source,

because the rules are subject to change.

AN EXAMPLE FROM COMPOUND INTEREST

Suppose that after 10 years, a $100 investment has grown to $160. What was

the annual return?

We need to find an interval that contains the 160 final value.

We try 3%, and find the value is 134.39, so

We try 4%, and find the value is 148.02, so

We try 5%, and find the value is 162.08, and we have our desired

interval, [4, 5].

We bisect the interval, and

Try 4.5%, and find the value is 155.30, so we bisect the interval [4.5, 5],

and

Try 4.75%, and find the value is 159.05, so we bisect the interval [4.75,

5], and

Try 4.875, and find the value is 160.96,

We decide we are close enough, so we bisect the interval [4.75, 4.875]

and obtain 4.8125 as the approximate interest rate. We are within

.0625 of the correct answer.

36 Compound Interest