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 April 10th, 2017, 09:19 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 SamSeymour Algebra 3 February 4th, 2014 12:49 PM arron1990 Algebra 3 August 14th, 2012 04:50 AM Jakarta Algebra 3 August 4th, 2012 10:45 AM wulfgarpro Algebra 5 April 14th, 2010 01:13 AM arron1990 Calculus 1 December 31st, 1969 04:00 PM

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