Performance of advanced stock price models when it becomes exotic: an empirical study

We calibrate several advanced stock price models to a time series of real market data European options on the DAX. Via Monte Carlo simulation, we barrier down-and-out call for all and compare modeled prices given options. The Bates model reproduces option very well. BNS overvalues Lévy with stochastic time-change leverage undervalue exotic Heston local volatility by about 5–6%. A heuristic analysis suggests that different degree fluctuation random paths are responsible producing Higher margins or additional risks like liquidity, calibration risk might economically explain why many