In this paper we use the Malliavin calculus techniques to obtain an expression for the short-time behavior of the at-the-money implied volatility skew for a generalization of the Bates model, where the volatility does not need to be neither a difussion, nor a Markov process, as the examples in section 7 show. This expression depends on the derivative of the volatility in the sense of Malliavin calculus.

In this paper we use the Malliavin calculus techniques to obtain an expression for the short-time behavior of the at-the-money implied volatility skew for a generalization of the Bates model, where the volatility does not need to be neither a difussion, nor a Markov process, as the examples in section 7 show. This expression depends on the derivative of the volatility in the sense of Malliavin calculus.

In this paper we introduce a Stratonovich type stochastic integral with respect to the fractional Brownian motion with Hurst parameter less than 1/2. Using the techniques of the Malliavin calculus, we provide sufficient conditions for a process to be integrable. We deduce an Itô formula and we apply these results to study stochastic differential equations driven by a fractional Brownian motion with Hurst parameter less than 1/2.

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In this paper we consider a financial market with an insider that has, at time t = 0, some additional information of the whole developing of the market. We use the forward integral, which is an anticipating integral, and the techniques of the Malliavin calculus so that we can take advantage of the privileged information to maximize the expected logarithmic utility from terminal wealth.KEY WORDS: derivative operator in the Malliavin calculus sense, forward and Skorohod integrals, optimal portfolio, expected utility