微笑校准：一种基于Mellin变换的挥发性面校准方法

IF 2.5 Q2 ECONOMICS

Econometrics and Statistics Pub Date : 2025-10-01 DOI:10.1016/j.ecosta.2022.05.004

M. Rodrigo , A. Lo

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引用次数: 0

摘要

布莱克-斯科尔斯框架中的隐含波动率不是一个常数，而是执行价格（“微笑/倾斜”）和到期时间的函数。一种流行的恢复波动面的方法是通过Dupire方程使用确定性波动函数模型。提出了一种基于Mellin变换的挥发性曲面标定方法。利用看涨期权价格相对于执行价格的梅林变换，给出了波动面的显式表达式，并给出了数值算法。给出了数值模拟结果，并对该方法的稳定性进行了数值验证。提出的Mellin变换方法提供了先前文献中给出的波动面广义形式的更简单和更直接的拟合。

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Calibrating with a smile: A Mellin transform approach to volatility surface calibration

The implied volatility in the Black-Scholes framework is not a constant but a function of both the strike price (“smile/skew”) and the time to expiry. A popular approach to recovering the volatility surface is through the use of deterministic volatility function models via Dupire’s equation. A new method for volatility surface calibration based on the Mellin transform is proposed. An explicit formula for the volatility surface is obtained in terms of the Mellin transform of the call option price with respect to the strike price, and a numerical algorithm is provided. Results of numerical simulations are presented and the stability of the method is numerically verified. The proposed Mellin transform approach provides a simpler and more direct fitting of generalised forms of the volatility surface given previously in the literature.

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来源期刊

Econometrics and Statistics ECONOMICS-

CiteScore

3.10

自引率

10.50%

发文量

期刊介绍： Econometrics and Statistics is the official journal of the networks Computational and Financial Econometrics and Computational and Methodological Statistics. It publishes research papers in all aspects of econometrics and statistics and comprises of the two sections Part A: Econometrics and Part B: Statistics.