Deduce which rate has larger standard deviation

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Reference no: EM131243487

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%, | y_SB - y_AM |_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 yis usually defined as the standard deviation of its logarithm, and can be well approximated by . By differentiating your answer to (a), derive an expression for the ratio of the volatility of yAM to the volatility of y_SB, assuming that the current level of rates is y_SB = 6%. Compare your answer to your empirical result from (b).

Reference no: EM131243487

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