Most viewed recipes tagged "laplace" but not "numerical"http://code.activestate.com/recipes/tags/laplace-numerical/views/2010-04-06T13:26:02-07:00ActiveState Code RecipesPricing Asian options using mpmath (Python)
2009-11-13T01:28:24-08:00Fernando Nieuwveldthttp://code.activestate.com/recipes/users/4172088/http://code.activestate.com/recipes/576954-pricing-asian-options-using-mpmath/
<p style="color: grey">
Python
recipe 576954
by <a href="/recipes/users/4172088/">Fernando Nieuwveldt</a>
(<a href="/recipes/tags/computational_finance/">computational_finance</a>, <a href="/recipes/tags/laplace/">laplace</a>, <a href="/recipes/tags/mpmath/">mpmath</a>).
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<p>I present a numerical method for pricing Asian options. The method is based on the numerical inversion of the Laplace transform. The inversion method that is used is based on Talbot contours. It is known that Geman and Yor's formula is computational expensive for low volatility cases. By using Talbots method we can reduce the timing for the low volatility cases, at least to \sigma ~ 0.05. Afterwards the method start to converge slowly. In the literature for \sigma = 0.1 the Geman and Yor formula converges slowly.</p>
Solving the Black-Scholes PDE with laplace inversion:Revised (Python)
2010-04-06T13:26:02-07:00Fernando Nieuwveldthttp://code.activestate.com/recipes/users/4172088/http://code.activestate.com/recipes/577142-solving-the-black-scholes-pde-with-laplace-inversi/
<p style="color: grey">
Python
recipe 577142
by <a href="/recipes/users/4172088/">Fernando Nieuwveldt</a>
(<a href="/recipes/tags/black/">black</a>, <a href="/recipes/tags/laplace/">laplace</a>, <a href="/recipes/tags/scholes/">scholes</a>, <a href="/recipes/tags/talbot/">talbot</a>).
Revision 2.
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<p>I originally posted this code in <a href="http://code.activestate.com/recipes/577132/">Recipe 577132</a> and this is a repost of that recipe with corrections since there was an error in the original recipe. Added here is an error analysis to show the effectiveness of the Laplace inversion method for pricing European options. One can test the accuracy of this method to the finite difference schemes. The laplace transform of Black-Scholes PDE was taken and the result was inverted using the Talbot method for numerical inversion. For a derivation of the laplace transform of the Black-Scholes PDE, see for instance <a href="http://www.wilmott.com/pdfs/020310_skachkov.pdf." rel="nofollow">www.wilmott.com/pdfs/020310_skachkov.pdf.</a></p>