Jump Size Distributions and Option Pricing

Growing evidences suggest two violations of Black, Scholes (J Polit Econ 81:3, 637–654, 1973) model: the downwards sloping volatility smile across moneyness and the heavy-tailed asset return distribution implied by option prices. Both abnormalities are caused by the existence of rare disasters or tail events in asset returns. Rubinstein (J Financ 49, 771–818, 1994) find that the implied volatility across moneyness becomes skewed since October 1987. This feature is often referred to as “volatility smirk”. On the other hand, (Jackwerth, Rubinstein, J Financ 51, 1161–1631, 1996) show that the option implied probability distribution is more left-skewed and changes from platykurtic to leptokurtic after the market crash in 1987.