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In this paper we study the short-time behavior of the at-the-money implied volatility for arithmetic Asian options with fixed strike price. The asset price is assumed to follow the Black-Scholes model with a general stochastic volatility…

Mathematical Finance · Quantitative Finance 2024-03-05 Elisa Alòs , Eulalia Nualart , Makar Pravosud

We derive an explicit asymptotic approximation for implied volatilities of caplets under the assumption that the short-rate is described by a generic quadratic term-structure model. In addition to providing an asymptotic accuracy result, we…

Mathematical Finance · Quantitative Finance 2022-12-09 Matthew Lorig , Natchanon Suaysom

We present small-time implied volatility asymptotics for Realised Variance (RV) and VIX options for a number of (rough) stochastic volatility models via large deviations principle. We provide numerical results along with efficient and…

Mathematical Finance · Quantitative Finance 2020-11-03 Chloe Lacombe , Aitor Muguruza , Henry Stone

In this paper, we study the martingale property for a Scott correlated stochastic volatility model, when the correlation coefficient between the Brownian motion driving the volatility and the one driving the asset price process is…

Probability · Mathematics 2016-06-14 Khadija Akdim , M'hamed Eddahbi , Mouna Haddadi

Several asymptotic results for the implied volatility generated by a rough volatility model have been obtained in recent years (notably in the small-maturity regime), providing a better understanding of the shapes of the volatility surface…

Mathematical Finance · Quantitative Finance 2022-11-16 Florian Bourgey , Stefano De Marco , Peter K. Friz , Paolo Pigato

Recent literature seek to forecast implied volatility derived from equity, index, foreign exchange, and interest rate options using latent factor and parametric frameworks. Motivated by increased public attention borne out of the…

Statistical Finance · Quantitative Finance 2020-09-22 Fearghal Kearney , Han Lin Shang , Lisa Sheenan

This note continues investigation of randomness-type properties emerging in idealized financial markets with continuous price processes. It is shown, without making any probabilistic assumptions, that the strong variation exponent of…

Trading and Market Microstructure · Quantitative Finance 2010-11-25 Vladimir Vovk

We develop closed-form expansions for the implied volatility of VIX options within the class of forward variance models. Our approach builds on weak-approximation techniques for VIX option prices and yields explicit implied volatility…

Computational Finance · Quantitative Finance 2026-05-26 Ying Liao , Ankush Agarwal , Florian Bourgey

The left tail of the implied volatility skew, coming from quotes on out-of-the-money put options, can be thought to reflect the market's assessment of the risk of a huge drop in stock prices. We analyze how this market information can be…

Risk Management · Quantitative Finance 2016-08-16 Ronnie Sircar , Stephan Sturm

The implied volatility skew has received relatively little attention in the literature on short-term asymptotics for financial models with jumps, despite its importance in model selection and calibration. We rectify this by providing…

Mathematical Finance · Quantitative Finance 2015-12-15 José E. Figueroa-López , Sveinn Ólafsson

A robust implementation of a Dupire type local volatility model is an important issue for every option trading floor. Typically, this (inverse) problem is solved in a two step procedure : (i) a smooth parametrization of the implied…

Pricing of Securities · Quantitative Finance 2011-05-09 Peter Friz , Stefan Gerhold

We introduce a new class of local volatility models. Within this framework, we obtain expressions for both (i) the price of any European option and (ii) the induced implied volatility smile. As an illustration of our framework, we perform…

Computational Finance · Quantitative Finance 2012-11-12 Matthew Lorig

Black-Scholes implied volatility is a quantile. The insight follows from the normalized option price being a probability on the variance scale, with the inverse Gaussian distribution providing the link. It enables analytically exact and…

Mathematical Finance · Quantitative Finance 2026-05-19 Wolfgang Schadner

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

We consider a stochastic volatility model which captures relevant stylized facts of financial series, including the multi-scaling of moments. The volatility evolves according to a generalized Ornstein-Uhlenbeck processes with super-linear…

Probability · Mathematics 2017-07-07 Francesco Caravenna , Jacopo Corbetta

Motivation for this paper is to understand the impact of information on asset price bubbles and perceived arbitrage opportunities. This boils down to study optional projections of $\mathbb{G}$-adapted strict local martingales into a smaller…

Mathematical Finance · Quantitative Finance 2020-03-24 Francesca Biagini , Andrea Mazzon , Ari-Pekka Perkkiö

We study the shapes of the implied volatility when the underlying distribution has an atom at zero and analyse the impact of a mass at zero on at-the-money implied volatility and the overall level of the smile. We further show that the…

Pricing of Securities · Quantitative Finance 2017-05-04 Stefano De Marco , Caroline Hillairet , Antoine Jacquier

The implied volatility smile surface is the basis of option pricing, and the dynamic evolution of the option volatility smile surface is difficult to predict. In this paper, attention mechanism is introduced into LSTM, and a volatility…

Computational Finance · Quantitative Finance 2019-12-25 Shengli Chen , Zili Zhang

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

We show that the frequent claim that the implied tree prices exotic options consistently with the market is untrue if the local volatilities are subject to change and the market is arbitrage-free. In the process, we analyse -- in the most…

Statistical Mechanics · Physics 2008-12-10 Karl Strobl