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首页> 外文会议>Proceedings of the Third IASTED International Conference on Financial Engineering and Applications >EFFICIENT CALIBRATION OF TIME-CHANGED L′EVY MODELS TO FORWARD IMPLIED VOLATILITY SURFACES
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EFFICIENT CALIBRATION OF TIME-CHANGED L′EVY MODELS TO FORWARD IMPLIED VOLATILITY SURFACES

机译：时变L'EVY模型对​​隐含波动率表面的有效校准

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摘要

Time-changed L′evy models are capable of accurately calibrating implied volatilities of plain vanilla options across strikes and maturities at a fixed point in time, a feature that distinguishes them from most other classes of option pricing models. However, the quality of a pricing model is not only determined by its static fitting capabilities, but also by its dynamic properties, in particular if it is to be applied to the pricing of exotic derivatives. In this paper, we investigate the dynamic properties of a popular time-changed L′evy model by first calibrating it to a set of S&P 500 index options and then studying the forward implied volatilities it gives rise to.Themain tools in our endeavor are forward characteristic functions in conjunction with the Fast Fourier Transform(FFT) approach to option pricing. After showing how to adapt the FFT-approach to the pricing of forward start options and to the efficient computation of forward implied volatility surfaces, we derive the forward characteristic functions for our model. We find that forward implied volatility surfaces are largely undetermined for amodel that is calibrated to vanilla options only, and show how a trader can take advantage of this indeterminacy by incorporating his personal view of the future in the calibration. Our theoretical discussion is supplemented by numerical and graphical illustrations.
机译：时变的L'evy模型能够在固定的时间点精确地计算行权价和到期日之间普通香草期权的隐含波动率，这一功能使它们与大多数其他类别的期权定价模型区分开来。但是，定价模型的质量不仅取决于其静态拟合能力，还取决于其动态属性，尤其是要应用于外来衍生产品的定价时。在本文中，我们通过先将流行的时变L'evy模型校准为一组标准普尔500指数期权，然后研究其产生的正向隐含波动率，来研究其动态性质。特征功能与快速傅立叶变换（FFT）方法一起用于期权定价。在展示了如何使FFT方法适应正向启动期权的定价以及正向隐含波动率面的有效计算之后，我们得出了模型的正向特征函数。我们发现，对于仅针对原始期权进行过校准的模型，前向隐含波动率面在很大程度上不确定，并且表明交易者如何通过将自己对未来的看法纳入校准中来利用不确定性。我们的理论讨论辅以数字和图形插图。

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