Beyond epicycles: models must describe markets, not just fit them
Modelling needs to embrace complexity in volatility patterns, says Jean-Philippe Bouchaud
When Bruno Dupire proposed his celebrated local volatility model in 1994, it spread like wildfire among practitioners.
No wonder. It preserves all the seductions of Black–Scholes’ near-magical delta hedge and, with limited numerical effort, can be calibrated to any surface of traded European option prices – simply by letting volatility depend on price level and time. When such a congenial quick
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