- Date: 9 Dec. (Thu.)
- Place: On the Web
- Time: 16:30 – 18:00
- Speaker: Takwa Saidaoui (University of Tunis El Manar)
- Title: Behavior of some discrete hedging errors in finance; a Fourier estimator in the presence of asynchronous trading
- Abstract:
This thesis focuses on three topics of financial mathematics. The first part consists of a study of the L^2-norm asymptotic behavior of the error due to the replicating portfolio discretization. The averaging feature of the Asian-type payoff plays a crucial role in improving the convergence rate of the error. We show that the achieved order is explicitly related to the fractional regularity of the payoff function. The second part studies the convergence rate of the error due to the discretization of the Clark-Ocone representation for functions of Levy processes with pure jumps. The obtained rate is strongly related to the regularity index of the Sobolev space to which the payoff belongs. The last part is a study of the asymptotic behavior (central limit theorem, CLT) of the Fourier estimator of the integrated covariance under the assumption of data asynchronicity. Thus, for a determinate choice of parameters, the estimator is consistent and the CLT is valid for a sub-optimal rate.
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