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B rownian motion and normal distribution have been widely used in the Black-Scholes option-pricing framework to model the return of assets. However, two puzzles emerge from many empirical investigations: the leptokurtic feature that the return distribution of assets may have a higher peak and two (asymmetric) heavier tails than those of the normal distribution, and an empirical phenomenon called "volatility smile" in option markets. To incorporate both of them and to strike a balance betweendoi:10.1287/mnsc.48.8.1086.166 fatcat:xx6mnjvjifeztgal7wcocpfyom