
Economics Economics Forum  Financial Mathematics, Econometrics, Operations Research, Mathematical Finance, Computational Finance 
 LinkBack  Thread Tools  Display Modes 
April 27th, 2014, 11:51 PM  #1 
Member Joined: Oct 2009 Posts: 50 Thanks: 0  how to derive log approximation?
Hello! This is probably an easy question. I'm trying to find out how to derive the log approximation of an exchange rate percentage change. So the actual change is: ( S[t+1]  St )/St How do you derive from this that an approximation is log(St+1)  log(St)? Thank you! 
May 2nd, 2014, 08:52 PM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038  
May 2nd, 2014, 09:30 PM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,674 Thanks: 2654 Math Focus: Mainly analysis and algebra 
I think the OPs equation is not as you worked on, but $$\frac{s_{t+1}  s_t}{s_t} = \frac{s_{t+1}}{s_t}1$$ Although, $$\log{\frac{s_{t+1}  s_t}{s_t}} = \log{\left(s_{t+1}  s_t\right)}  \log{s_t}$$ I don't know what the question is either. Last edited by v8archie; May 2nd, 2014 at 09:33 PM. 
May 3rd, 2014, 11:03 PM  #4  
Member Joined: Oct 2009 Posts: 50 Thanks: 0  Quote:
The thing is, my textbook does this "derivation"/aproximation (the factis,I don't know what their doing...): They assume: $${rr*} = \frac{S_{t+1}S_{t}}{S_t}$$ And conclude from this that (This step I don't get): $$rr* = \log{S_{t+1}}  \log{S_t}$$ I understand your derivation, but its different from my textbook, since they don't take the log on both sides. They're effectively saying: $$\frac{S_{t+1}S_{t}}{S_t} = \log{S_{t+1}}  \log{S_t}$$ And I don't understand why that would be true (or approximately true, since I don't know if its an aproximation or not.) I hope my question is clearer now. Thanks for the help, either way! Last edited by questioner1; May 3rd, 2014 at 11:10 PM.  

Tags 
approximation, derive, log 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Derive  Solarmew  Applied Math  16  May 2nd, 2012 09:09 PM 
Derive this  dudetheman  Calculus  2  January 18th, 2012 11:44 AM 
how do I derive this  dmxnemesis  Calculus  4  October 20th, 2010 03:38 PM 
How to derive e?  NeuroFuzzy  Calculus  14  September 18th, 2010 10:35 PM 
Derive x/y  instereo911  Calculus  2  October 8th, 2009 02:55 PM 