Abstract
Stock option prices contain forecasting information about stock price volatility and potentially, the probability of default. So, we use BAC stock option market data to research whether future realized volatility is explained by two types of model-free implied volatility ( MFIV ) . Here are our two MFIV estimations. We adopt a risk-neutral density ( RND ) model consisting of a mixture of lognormal densities with probability of bankruptcy term ( MLNbk2 ), and a mixture of lognormal ( MLN ) to estimate model-free implied volatility, and the realized volatility ( RV ) we want to know whether we add in the probability of bankruptcy term, it can have significant effect to estimate realized volatility. After our experiment, we can conclude that MLNbk2 is better than MLN, we can say for forcasting realized volatility, add bankruptcy rate is better than not adding.