The Black-Scholes model assumes a normal distribution of returns. However, non-normal skewness and kurtosis are found to contribute significantly to the phenomenon of volatility smile.
Compared with the normal probability density function, the Gram-Charlier model allows for more flexibility because it uses skewness and kurtosis as input parameters. Montgomery Investment Technology provides Online Calculators for option pricing implementing the Gram-Charlier model.
Skewness and kurtosis can be calculated from historical stock prices. Also, the market prices of call and put European options ...
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