|Author||Topic: crazy e|
|Help. Can somebody explain the diff. btwn discounting something by dividing by ((1+discount rate)^t) and this crazy e. For example: 100/(1+.05)^2 vs. 100xe^(-.05x2)? Something about continuous compounding, but I can't find an explanation. Please spare the crazy math, if possible.|
|I can see how you are confused!
First 'e' is a constant equivilant to 2.71828 (on your calc press '1' '2nd' 'e' and you will get 2.71828 etc.. Why? ask me and I might tell ya, but u said no crazy math!
In scientific notation occaisionally we use '1e4' which is 1000 (use an Excel spreadsheet to do this).
So you should know what you are looking at 'e' an exponential (first description) or 'e' and exponent (second description)!
|If you are given a "Continuous compounding" rate, that is when the "e" math comes into play. For example, if you are given an equity forward (or futures) question and they give you the continuously compounded dividend yield (CCDY), you would discount the "spot" price at the CCDY, then compound the result of that at the risk-free rate (RFR).
So you'd take the spot rate times "e" raised to the power of: (the negative of the CCDY)*(time), for the first part, or
Then you'd compound that at the RFR. But, keep in mind that when given a question w/ CCDY, you need to take the LN of the "continuous" RFR first. They may or may not tell you that the RFR is continuous, but it is. (They may use the term "discrete" interest also.) To get the plain RFR, simply take LN(1+RFR). Then you can compound the discounted spot price from above at:
to get the fwd price.
Why is the "e" formula for the first part negative? Because we are discounting. It is positive for the second part because we are compounding.
This format also holds true for other problems where we are given continuous compounding or discrete interest.
I don't think we'd see it on bond futures/forwards, but we certainly would on currency futures/forwards as well as any option questions. Hope this helps.