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*Question*: Daycount and Frequency Two market standards
for US dollar interest rates are semi-annual compound...

Daycount and Frequency

Two market standards for US dollar interest rates are
semi-annual compounding with 30/360 daycount (semi-bond, denoted
y_{SB}), and annual compounding with act/360 daycount
(annual-money, denoted y_{AM}).

(a) Derive an expression for y_{AM} in terms of
y_{SB} . You can assume all years have 365 days.

(b) Show that when y_{SB} = 6%,
< 0.01%. Calculate y_{AM} for the cases y_{SB}
= 5% and y_{SB} = 7% and use your answers to deduce which
rate has larger standard deviation.

(c) The volatility of a rate y is usually defined as the
standard deviation for its logarithm, and can be well approximated
by
. By differentiating your answer to (a), derive an expression for
the ratio of the volatility of y_{AM} to the volatility of
y_{SB}, assuming that he current level of rates is
y_{SB} = 6%. Compare your answer to your empirical result
from (b).