How to convert an interest rate from bank discount basis to continuous compounding

Question

I read on Investopedia that a 360-day-count convention is being used in the case of Bank Discount Basis. And I found the following formula on Wikipedia:

R = n*ln(1 + r/n)

This is the conversion formula for converting an interest rate r with compounding frequency n to the rate R on a continuous compounding basis. What I wonder is if it is correct to set r equal to the interest rate on the Bank Discount Basis. And n equal to 360. Would that give me the conversion formula for converting from Bank Discount Basis to continuous compounding?

Answer 1

I recently found the answer to my own question! =) I realized that I had to be even more stubborn than I usually am. =S

I think that this web page is great for learning how to calculate:

http://www.allbusiness.com/glossaries/discount-yield/4952922-1.html

Let's say for instance that the 3-month rate given on discount basis is 1.3 %. Then I can calculate it on the continuous compounding basis by first calculating the discount factor:

0.013*90/360 = 0.00325 => d = 1 - 0.00325 = 0.99675

Then I get the rate that I want by the following calculation:

-1*(360/90)*ln(d) = 1.302117 %

The math here is very simple but it is essential to find the relevant formulas first.