Explicit Föllmer--Schweizer decomposition and discretization with jump correction in exponential Lévy models

Nguyen Tran Thuan

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arXiv · 2009.04328

Explicit Föllmer--Schweizer decomposition and discretization with jump correction in exponential Lévy models

Nguyen Tran Thuan

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Abstract

We investigate two hedging problems in exponential Lévy models. First, we provide an explicit representation for the Föllmer--Schweizer decomposition of European type options under mild conditions, which implies a closed-form expression of the corresponding local risk-minimizing strategies. Secondly, we discretize stochastic integrals driven by an exponential Lévy process using a jump correction method. The convergence rate of the resulting discretization error as the expected number of discretization times increases is measured in weighted BMO spaces, implying also $L_p$-estimates, $p \in (2, \infty)$. Moreover, the effect of a change of measure satisfying a reverse Hölder inequality is addressed. As an application, the error caused by discretizing the local risk-minimizing strategies is investigated in dependence of properties of the Lévy measure, the regularity of the payoff function and the chosen random discretization times.

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BibTeX RIS

Nguyen Tran Thuan. 2022-10-02. Explicit Föllmer--Schweizer decomposition and discretization with jump correction in exponential Lévy models. https://arxiv.org/abs/2009.04328

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