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We study specific nonlinear transformations of the Black-Scholes implied volatility to show remarkable properties of the volatility surface. Model-free bounds on the implied volatility skew are given. Pricing formulas for the European…

Pricing of Securities · Quantitative Finance 2010-09-30 Masaaki Fukasawa

The Black-Scholes model gives vanilla Europen call option prices as a function of the volatility. We prove Lipschitz stability in the inverse problem of determining the implied volatility, which is a function of the underlying asset, from a…

Analysis of PDEs · Mathematics 2013-02-05 Mourad Bellassoued , Raymond Brummelhuis , Michel Cristofol , Eric Soccorsi

We price European options in a class of models in which the volatility of the underlying risky asset depends on the short rate of interest. Our study results in an explicit pricing formula that depends on knowledge of a characteristic…

Mathematical Finance · Quantitative Finance 2026-02-03 Tim Leung , Matthew Lorig

In this paper, we study the relationship between the short-end of the local and the implied volatility surfaces. Our results, based on Malliavin calculus techniques, recover the recent $\frac{1}{H+3/2}$ rule (where $H$ denotes the Hurst…

Mathematical Finance · Quantitative Finance 2023-09-18 Elisa Alòs , David García-Lorite , Makar Pravosud

Recent empirical studies suggest that the volatilities associated with financial time series exhibit short-range correlations. This entails that the volatility process is very rough and its autocorrelation exhibits sharp decay at the…

Pricing of Securities · Quantitative Finance 2018-04-17 Josselin Garnier , Knut Solna

We consider the asymptotic behavior of the implied volatility in stochastic asset price models with atoms. In such models, the asset price distribution has a singular component at zero. Examples of models with atoms include the constant…

Pricing of Securities · Quantitative Finance 2013-11-26 Archil Gulisashvili

We derive the short-maturity asymptotics for prices of options on realized variance in local-stochastic volatility models. We consider separately the short-maturity asymptotics for out-of-the-money and in-the-money options cases. The…

Pricing of Securities · Quantitative Finance 2025-11-19 Dan Pirjol , Xiaoyu Wang , Lingjiong Zhu

In this paper we use Malliavin Calculus techniques in order to obtain expressions for the short-time behavior of the at-the-money implied volatility (ATM-IV) level and skew for a jump-diffusion stock price. The diffusion part is assumed to…

Mathematical Finance · Quantitative Finance 2025-03-31 Elisa Alòs , Òscar Burés , Josep Vives

This paper investigates short-term behaviors of implied volatility of derivatives written on indexes in equity markets when the index processes are constructed by using a ranking procedure. Even in simple market settings where stock prices…

Pricing of Securities · Quantitative Finance 2025-03-11 Huy N. Chau , Duy Nguyen , Thai Nguyen

The article is devoted to models of financial markets with stochastic volatility, which is defined by a functional of Ornstein-Uhlenbeck process or Cox-Ingersoll-Ross process. We study the question of exact price of European option. The…

Pricing of Securities · Quantitative Finance 2016-08-02 S. Kuchuk-Iatsenko , Y. Mishura , Y. Munchak

In the paper written by Klibanov et al, it proposes a novel method to calculate implied volatility of a European stock options as a solution to ill-posed inverse problem for the Black-Scholes equation. In addition, it proposes a trading…

Numerical Analysis · Mathematics 2025-01-29 Wanchaloem Wunkaew , Yuqing Liu , Kirill V. Golubnichiy

In this note, we develop stock option price approximations for a model which takes both the risk o default and the stochastic volatility into account. We also let the intensity of defaults be influenced by the volatility. We show that it…

Computational Engineering, Finance, and Science · Computer Science 2007-12-21 Erhan Bayraktar

This paper introduces the Inverse Gamma (IGa) stochastic volatility model with time-dependent parameters, defined by the volatility dynamics $dV_{t}=\kappa_{t}\left(\theta_{t}-V_{t}\right)dt+\lambda_{t}V_{t}dB_{t}$. This non-affine model is…

Computational Finance · Quantitative Finance 2019-06-28 Nicolas Langrené , Geoffrey Lee , Zili Zhu

Accurately characterizing the implied volatility curves is a central challenge in option pricing and risk management. The classical SABR model by Hagan et al. has been widely adopted in practice due to its well-defined stochastic volatility…

Mathematical Finance · Quantitative Finance 2026-03-31 Wenxuan Zhang , Zhouchi Lin , Benzhuo Lu

In this paper we study the short-maturity asymptotics of up-and-in barrier options under a broad class of stochastic volatility models. Our approach uses Malliavin calculus techniques, typically used for linear stochastic partial…

Probability · Mathematics 2026-05-11 Òscar Burés

We propose a new model for the forecasting of both the implied volatility surfaces and the underlying asset price. In the spirit of Guyon and Lekeufack (2023) who are interested in the dependence of volatility indices (e.g. the VIX) on the…

Computational Finance · Quantitative Finance 2025-10-15 Hervé Andrès , Alexandre Boumezoued , Benjamin Jourdain

In this paper, we obtain asymptotic formulas with error estimates for the implied volatility associated with a European call pricing function. We show that these formulas imply Lee's moment formulas for the implied volatility and the…

Pricing of Securities · Quantitative Finance 2009-06-03 A. Gulisashvili

This paper concerns a local volatility model in which volatility takes two possible values, and the specific value depends on whether the underlying price is above or below a given threshold value. The model is known, and a number of…

Mathematical Finance · Quantitative Finance 2024-05-17 Alexander Gairat , Vadim Shcherbakov

We derive an explicit asymptotic approximation for the implied volatilities of Call options written on bonds assuming the short-rate is described by an affine short-rate model. For specific affine short-rate models, we perform numerical…

Mathematical Finance · Quantitative Finance 2021-06-09 Matthew Lorig , Natchanon Suaysom

We present a rigorous study of the short maturity asymptotics for Asian options with continuous-time averaging, under the assumption that the underlying asset follows a local volatility model. The asymptotics for out-of-the-money,…

Pricing of Securities · Quantitative Finance 2016-12-16 Dan Pirjol , Lingjiong Zhu