自分解Lévy模型的标定
Calibration of self-decomposable Lévy models
摘要：
研究了具有无穷跳活动的指数Lévy模型的非参数校正问题。特别是我们的分析适用于自分解的过程，其跳跃密度的特点是由$k$ -功能，这是典型的非光滑在零。一方面估计漂移的活动措施$α:=k(0+)+k(0-)$和类似的参数的衍生物的$k$ -函数被认为是另一方面，我们估计非参数的$k$ -函数。最小最大收敛速度。由于利率依赖于$α$，我们构造估计适应这个未知的参数。我们的估计方法是基于观察到的期权价格的谱表示和通过切断高频的正则化。最后，该程序被应用到模拟和实际数据。
英文摘要：
We study the nonparametric calibration of exponential Lévy models with infinite jump activity. In particular our analysis applies to self-decomposable processes whose jump density can be characterized by the $k$-function, which is typically nonsmooth at zero. On the one hand the estimation of the drift, of the activity measure $α:=k(0+)+k(0-)$ and of analogous parameters for the derivatives of the $k$-function are considered and on the other hand we estimate nonparametrically the $k$-function. Minimax convergence rates are derived. Since the rates depend on $α$, we construct estimators adapting to this unknown parameter. Our estimation method is based on spectral representations of the observed option prices and on a regularization by cutting off high frequencies. Finally, the procedure is applied to simulations and real data.
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