, nor a Markov process as the examples in section 7 show. This expression depends on the derivative of the volatility in the …-the-money implied volatility skew for a generalization of the Bates model, where the volatility does not need to be neither a difussion …

volatility under a jump-diffusion stochastic volatility model, has no effect on the short-time behaviour of the at …-the-money implied volatility skew, although the corresponding Hull and White formula depends on the jumps. Towards this end, we use …

closed-form approximation formulas depending on the derivative operator. The numerical analysis shows that these formulas are …

implied volatility for very short maturities. Using this approximation we accurately calibrate the full set of parameters of …

volatility process is defined by means of a fractional integration of a diffusion process. This model preserves the short …-Scholes formula with volatility parameter equal to the root-mean-square future average volatility plus a term due to correlation and a … term due to the volatility of the volatility. This decomposition procedure does not need the volatility process to be …

We see that the price of an european call option in a stochastic volatility framework can be decomposed in the sum of … four terms, which identify the main features of the market that affect to option prices: the expected future volatility …, the correlation between the volatility and the noise driving the stock prices, the market price of volatility risk and the …