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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)*(taut) val2 = exp(alpha*(taut)*(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(taut)) / exp(val1+g*vol*sqrt(taut)) / val2 I CANT see how (note: , vol is $\sigma$, a is $\alpha$, K is $X$, (taut) is $\tau$.) Code: g: exp(g*g/2)  val3 / (val1+g*vol*sqrt(taut)) / exp(val1+g*vol*sqrt(taut)) / val2 log(e^x) = x. If you write out the code : 

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