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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 ySB), and annual compounding with act/360 daycount (annual-money, denoted yAM).

(a) Derive an expression for yAM in terms of ySB . You can assume all years have 365 days.

(b) Show that when ySB = 6%, lys B yAMI < 0.01%. Calculate yAM for the cases ySB = 5% and ySB = 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 dy . By differentiating your answer to (a), derive an expression for the ratio of the volatility of yAM to the volatility of ySB, assuming that he current level of rates is ySB = 6%. Compare your answer to your empirical result from (b).

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