Fix Dupire local volatility formula implementation

[CameronScarpati]

Summary

Corrected the implementation of Dupire's local volatility formula to properly use the Durrleman condition, which is the mathematically correct denominator for the formula.

Key Changes

• Updated formula documentation: Clarified that the denominator is the Durrleman condition g(k) rather than an inline expression
• Fixed denominator calculation: Changed from a linear combination to the correct squared term:
  • Old: 1 - k*w'/w + w''/2 - (w')²/4 * (1/w + 1/4)
  • New: (1 - k*w'/(2w))² - (w')²/4 * (1/w + 1/4) + w''/2
• Improved code clarity: Added explicit documentation of the Durrleman condition formula and reorganized the denominator calculation for better readability

Implementation Details

The key mathematical correction is in the denominator computation:

• The first term is now squared: (1 - k*w'/(2w))² instead of 1 - k*w'/w
• The coefficient in the first term changed from w' to w'/(2w)
• Term ordering was adjusted for clarity while maintaining mathematical equivalence

This ensures the local volatility calculation correctly implements Dupire's 1994 formula with the Durrleman condition.

https://claude.ai/code/session_01ExtzDyMXtMSUSjghYLyy2C