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 April 10th, 2017, 09:24 AM #1 Member   Joined: Sep 2013 Posts: 83 Thanks: 0 Help me understand simplification I am trying to figure out a python code, the problem is not the code but mathematics. First, we have equation (22): $${\textstyle{{{S_c}} \over X}} = {e^{ - (r + (1/2){\sigma ^2})\tau - g\sigma \sqrt \tau }}$$ where (23): $$g = \pm \sqrt {2\log {{{\sigma ^2}} \over {{{2r} \over {\sqrt a }}x\log x{e^{ - a{{(r + (1/2){\sigma ^2})}^2}\tau /(2{\sigma ^2})}}}}}$$ where $$a = 1 - {A \over {1 + {{{{(1 + \gamma )}^2}} \over 4}{\gamma ^2}\tau }}, A = {1 \over 2}{\left( {{\gamma \over {1 + \gamma }}} \right)^2}$$ and $$x = {X \over {{S_c}}},\gamma = {{2r} \over {{\sigma ^2}}}$$ NOW, to the question, Here is the Python code: Code:  alpha = 1.0 - ( .5 * gamma * gamma / (1.0 + gamma)**2 ) / ( 1.0 + (1.0 + gamma)**2 * vol * vol * (tau - t) / 4.0 ) val1 = (r+.5*vol*vol)*(tau-t) val2 = exp(-alpha*(tau-t)*(r+.5*vol*vol)**2/(2*vol*vol)) val3 = vol*vol*sqrt(alpha)/r/2.0 func = lambda g: exp(g*g/2) - val3 / (val1+g*vol*sqrt(tau-t)) / exp(val1+g*vol*sqrt(tau-t)) / val2 I CANT see how (note: , vol is $\sigma$, a is $\alpha$, K is $X$, (tau-t) is $\tau$.) Code: g: exp(g*g/2) - val3 / (val1+g*vol*sqrt(tau-t)) / exp(val1+g*vol*sqrt(tau-t)) / val2 Represents equation (23)? Its obvious that he has tried to simplify the original equation, i asked the author and he gave me two hints that i should use :Log(x/y) = log x - log y and log(e^x) = x. If you write out the code :  Tags simplification, understand Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post Ku5htr1m Calculus 0 April 10th, 2017 09:19 AM Caesar95 Algebra 1 May 10th, 2015 03:01 AM 3uler Trigonometry 1 February 3rd, 2015 03:08 AM SamSeymour Algebra 3 February 4th, 2014 12:49 PM p3aul Algebra 5 January 23rd, 2011 09:11 PM

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