We introduce a discrete-time model for log-return dynamics with observable volatility and jumps. Our proposal extends … the class of Realized Volatility heterogeneous auto-regressive gamma (HARG) processes adding a jump component with time … compensating for equity, volatility, and jump risks, the generating function under the risk-neutral measure inherits analytical …

In a tractable stochastic volatility model, we identify the price of the smile as the price of the unspanned risks … traded in SPX option markets. The price of the smile reflects two persistent volatility and skewness risks, which imply a …-form and structural models of stochastic volatility …

premium. Empirical estimation exercises show that the GARCH option-pricing models under our mLRNVR are able to price the SPX … one-month variance swap rate, i.e., the CBOE Volatility Index (VIX) accurately. Our research suggests that one should use …