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首页> 外文期刊>Inverse Problems: An International Journal of Inverse Problems, Inverse Methods and Computerised Inversion of Data >Tikhonov regularization applied to the inverse problem of option pricing: convergence analysis and rates
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Tikhonov regularization applied to the inverse problem of option pricing: convergence analysis and rates

机译：Tikhonov正则化应用于期权定价的反问题：收敛分析和费率

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摘要

This paper investigates the stable identification of local volatility surfaces sigma (S, t) in the Black-Scholes/Dupire equation from market prices of European Vanilla options. Based on the properties of the parameter-to-solution mapping, which assigns option prices to given volatilities, we show stability and convergence of approximations gained by Tikhonov regularization. In the case of a known term-structure of the volatility surface, in particular, if the volatility is assumed to be constant in time, we prove convergence rates under simple smoothness and decay conditions on the true volatility. The convergence rate analysis sheds light onto the importance of an appropriate a priori guess for the unknown volatility and the nature of the ill-posedness of the inverse problem, caused by smoothing properties and the nonlinearity of the direct problem. Finally, the theoretical results are illustrated by numerical experiments.
机译：本文研究了从欧洲香草期权的市场价格中Black-Scholes / Dupire方程中稳定波动表面σ（S，t）的稳定识别。基于参数到解决方案映射的属性，该属性将期权价格分配给给定的波动率，我们展示了Tikhonov正则化的稳定性和收敛性。特别是在已知的挥发性表面的期限结构的情况下，如果假定挥发性在时间上是恒定的，我们将在真实的挥发性下，在简单的平滑度和衰减条件下证明收敛速度。收敛速度分析揭示了适当的先验猜测对未知波动性和反问题不适定性性质的重要性，该不确定性是由平滑问题和直接问题的非线性引起的。最后，通过数值实验说明了理论结果。

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