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Oct 7th, 2015
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  1. for i=(Asset_Steps):-1:2
  2.  
  3. % Discretizing The Option Value and Computing The Greeks
  4.  
  5. Delta= (V_Old(i + 1) - V_Old(i - 1)) / (2*ds);
  6.  
  7. Gamma= (V_Old(i + 1) - 2 * V_Old(i) + V_Old(i - 1)) / (ds*ds);
  8.  
  9. Theta = -0.5 * Sigma * Sigma * Stock(i) * Stock(i) * Gamma + ...
  10. R*(V_Old(i)-(Stock(i) * Delta)); % Black Scholes PDE Solving
  11.  
  12. V_New(i) = V_Old(i) - dt * Theta; % Explicit Scheme
  13.  
  14. end
  15.  
  16. % Boundary Conditions
  17.  
  18. V_New(1) = V_Old(1) * (1 - R * dt); % Lower Boundary
  19.  
  20. V_New(Asset_Steps+1) = 2 * V_New(Asset_Steps) - V_New(Asset_Steps - 1); % Upper Boundary
  21.  
  22. %Marching Backwards in T
  23.  
  24. V_Old=V_New;
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