I am studying the paper Arbitrage-Free Smoothing of the Implied Volatility Surface, from Matthias R. Fengler (https://core.ac.uk/download/pdf/6978470.pdf). The problem I want to solve is much simpler as I do not need a smoothed volatility surface but only a smoothed volatility smile. I will work with only one single future time $T$.

股票期权 波动率微笑曲线Volatility Smile of Equity Option 对股票期权来说，波动率微笑曲线呈现左高右低，期权隐含波动率随着行权价格升高逐渐降低。 原因：

2024年3月30日 · Ultimately, I am looking to implement a volatility smoothing model for an equity volatility skew for option-implied volatilities of European index options (mostly short-term maturity, think less than 60 days-to-maturity) with a focus on maximizing the number of option-implied volatilities (as a result of the inter/extrapolation and smoothing ...

波动率微笑（Volatility smiles）指期权隐含波动率（implied volatility）与行权价格（strike price）之间的关系。 波动率微笑现象是期权市场中常见的现象,对指导期权投资具有重要意义。

In finance, a common challenge is to the implied volatility smile function. Based on the assumption of a geometric Brownian motion governing the stock price dynamics, an unknown volatility parameter is implied from ob-served option prices using the Black and Scholes (1973) formula.

Deep smoothing focuses on applying deep learning methods to generate smooth, arbitrage-free implied volatility surfaces. For someone unfamiliar with quantitative finance, this problem can be summarized as follows: Imagine you are given a set of points \((k, \tau, iv)\) …

Focusing on these facts, this paper attempted to show which data observation window supplies the kurtosis and skewness which most effectively smoothes the volatility smile of Brazilian assets....

2021年1月18日 · Implied volatility surfaces and smiles constructed by fitting a cubic spline to raw market data may contain arbitrage. In fact, even if the market data points used do not contain arbitrage, cubic interpolation between data points may introduce it.

In finance, a common challenge is to the implied volatility smile function. Based on the assumption of a geometric Brownian motion governing the stock price dynamics, an unknown volatility parameter is implied from observed option prices using the Black and Scholes (1973) formula.

2018年11月4日 · Given the dynamics of the forward rate, the stochastic instantaneous volatility, and the Black model, we get an algebraic expression that the Black Implied Volatility must satisfy. Given traded and liquid options, we fit the SABR model on …