Volatility models must be rough to match market skew.
problem Inconsistent non-rough volatility models with power law volatility skew.
method Asymptotic expansion and continuous price dynamics analysis.
result Volatility must be rough to align with market skew.
Study local volatility from rough volatility models, finding new skew rule.
problem Understanding local volatility from rough volatility models.
method Analyzing asymptotic behavior of local volatility surface generated by rough stochastic volatility models.
result New skew rule: ratio of implied and local vol skews tends to 1/(H + 3/2).
Derives formula for skew stickiness ratio in asset price and volatility dynamics.
problem Capturing joint dynamics of asset price and volatility.
method Uses Itô-Wentzell and Clark-Ocone formulae to derive representation.
result Derives asymptotics of skew stickiness ratio under stochastic volatility models.
Study on skew and curvature of implied and local volatilities using Malliavin calculus.
problem Relationship between short-end of local and implied volatility surfaces.
method Malliavin calculus techniques
result Recover the $ rac{1}{H+3/2}$ rule for rough volatilities and relationships between skew and curvature.
Simple method solves Quanto Skew problem.
problem Quanto Skew problem in Equities and FX.
method Analytical method that accommodates Equity and FX volatility skew.
result Highly efficient and fast performance.
Paper derives new option pricing formulas and approximations for a local volatility model with discontinuity.
problem Modeling extreme ATM skew in a local volatility model with discontinuity.
method Uses joint distribution of Skew Brownian motion and its functionals to derive option pricing formulas and approximations.
result Derives an approximation of option prices by Black-Scholes prices, simplifying skew behavior.
Paper proves SVV model reproduces power-law skew in implied volatilities.
problem Reproducing power-law behavior in implied volatility skew.
method Analytical proof using Malliavin calculus and Volterra kernel selection.
result SVV model reproduces power-law skew under correct kernel choice.
Study shows different types of volatility and skewness changes affect stock prices.
problem Different types of volatility and skewness changes affect stock prices.
method Used intraday data for individual stocks to analyze cross-section of asset returns.
result Idiosyncratic transitory and persistent shocks to volatility and skewness are priced differently in stock returns.
Model captures SPX and VIX volatility surfaces and skew-stickiness ratio.
problem Capturing volatility dynamics in financial markets.
method Two-factor Quintic Ornstein-Uhlenbeck (OU) model with polynomial volatility.
result Model accurately represents SPX and VIX volatility surfaces and SSR.
DCNN improves volatility smile and skewness calibration without arbitrage constraints.
problem Calibrating volatility smile and skewness surfaces with no arbitrage constraints.
method Derivative-Constrained Neural Network (DCNN) incorporating derivatives in the loss function.
result DCNN generates a smooth surface that satisfies no-arbitrage conditions.
Using Malliavin Calculus techniques, we derive closed-form expressions for the at-the-money behaviour of the forward implied volatility, its skew and its curvature, in general Markovian stochastic volatility models with continuous paths.
Modified Jones-Faddy skew t-distribution captures asymmetry in stock returns.
problem Negative skew and positive mean in stock returns due to broken symmetry of stochastic volatility.
method Modified Jones-Faddy skew t-distribution applied to split gains and losses, using stochastic differential equations for stock returns and volatility.
result The modified distribution effectively captures the asymmetry in daily S&P500 returns, including its tails.
Enhanced SABR model captures complex volatility smiles in Chinese financial options.
problem Limited accuracy of classical SABR model in fitting implied volatility curves.
method Proposes skew-SABR model with an extended stochastic dynamics and a new Black implied volatility expression.
result Skew-SABR model achieves high and stable fitting accuracy across various market conditions.
Study on implied volatility of Asian options with stochastic volatility.
problem Understanding the implied volatility of Asian options under stochastic volatility models.
method Using Malliavin calculus and anticipating Ito's formula, the paper computes and finds asymptotic formulas for the implied volatility and skew.
result Developed short-maturity asymptotic formulas for the skew of the implied volatility, which depends on the roughness of the volatility model.
This paper proposes new GARCH models for cryptocurrency volatility, showing skewed distributions improve prediction accuracy.
problem Predicting cryptocurrency volatility and improving upon normality assumptions.
method Non-Gaussian GARCH models with Skewed Generalized Error Distribution.
result Skewed distributions enhance forecasting accuracy for cryptocurrency exchange rates.
There are some statistical anomalies in the Chinese stock market, i.e., positive return skewness, anti-leverage effect (positive returns induce higher volatility than negative returns); and reverse volatility asymmetry (contemporaneous return-volatility correlation is positive). In this paper, we first confirm the exis…
Model accurately calibrates FX market skew for exotic options.
problem Inconsistent prices from different models for FX derivatives.
method Fully parameterized local volatility model with numerical methods.
result Model provides reliable prices for daily trading.
Analyzes multi-day stock returns, showing linear volatility and mean dependence.
problem Linear dependence of volatility and mean in accumulated stock returns.
method Modified Jones-Faddy skew t-distribution analysis.
result Linear dependence of volatility and mean on the number of days of accumulation.
The paper improves asset allocation using a skew-normal distribution in the Black-Litterman model.
problem Improving asset allocation under skewed return distributions.
method Using the Black-Litterman model with hidden truncation skew-normal distribution and Simaan's three-moment risk model.
result Optimal portfolios have less risk and higher skewness compared to classical BL model.
Dynamic skewness models improve financial time series analysis.
problem Modeling financial time series with skewness and heavy tails.
method Dynamic skewness stochastic volatility models with penalized priors and HMC estimation.
result Penalized priors outperform classical choices in model performance.
The article develops a model for skewness risk in risk parity portfolios.
problem Managing skewness risk in asset allocation models.
method Modeling asset returns with skewness and jumps, deriving analytical formulas for risk contributions.
result Skewness-based risk parity portfolios outperform volatility-based portfolios in managing jump risks.
The paper examines short-term volatilities in equity indexes using a ranking procedure.
problem Understanding short-term behaviors of implied volatility in equity markets.
method Using a ranking procedure to model equity index dynamics, the paper investigates the short-term volatilities of derivatives written on indexes.
result The models reconcile the long memory of volatilities and power law of ATM skews in equity markets.
New rough stochastic volatility models using log-modulated fractional Brownian motion.
problem Analyzing rough stochastic volatility models over the range 0≤H<1/2. method Introducing log-modulated fractional Brownian motion (log-fBm) to handle H=0 and analyze over the full range. result Obtained skew asymptotics of log(1/T)−pTH−1/2 as To0 for H≥0, no flattening of skew as Ho0. Study on implied volatility of Inverse options under stochastic volatility models.
problem Short-time behavior and skew of implied volatility for Inverse European options.
method Malliavin calculus, anticipating Itô's formula, asymptotic analysis.
result Asymptotic formula for skew of implied volatility, extending to Quanto-Inverse options.
We develop a method to study the implied volatility for exotic options and volatility derivatives with European payoffs such as VIX options. Our approach, based on Malliavin calculus techniques, allows us to describe the properties of the at-the-money implied volatility (ATMI) in terms of the Malliavin derivatives of t…
We derive the joint density of a Skew Brownian motion, its last visit to the origin, local and occupation times. The result is applied to option pricing in a two valued local volatility model and in a displaced diffusion model with constrained volatility.
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 high-order asymptotic expansions for the at-the-money implied volatility skew, under a…
Modeling implied volatility surface dynamics with Hawkes kernels.
problem Understanding and predicting high-frequency dynamics of the implied volatility surface.
method Hawkes modeling of the volatility surface, with coefficients governing skew and convexity.
result Simple conditions on Hawkes kernel coefficients ensure no-arbitrage and reduce parameter estimation.
Study on short-term behavior of ATM-IV for jump-diffusion model.
problem Analyzing the short-time behavior of ATM-IV for a specific stochastic volatility model.
method Used Malliavin Calculus techniques to derive expressions for ATM-IV level and skew.
result Short-time behavior of ATM-IV level is consistent for all pure-jump Lévy processes.
Study shows how cryptocurrency market skewness and kurtosis interact during pandemic.
problem Understanding the dynamics of cryptocurrency markets during the pandemic.
method Examined skewness and kurtosis interactions in cryptocurrency market data.
result More observations cluster around extremes during pandemic, indicating volatile behavior.
The ADO-Heston model approximates market implied skew in vanilla options.
problem Reproduce market implied skew in vanilla options using a Markovian approximation.
method Derived characteristic function under risk-neutral and real measures, chose market price of risk, found closed form for log-price CF and implied skew.
result The ADO-Heston model can approximate the vanilla implied skew at small T but not exactly as rough volatility models. New inflation model captures correlations and skew in interest rates.
problem Modeling inflation with market correlations and skew.
method Multi-factor volatility structure with parametric correlation calibration, leveraging single-factor Gaussian model.
result Captures market volatility skew with a single process, simplifying model calibration.
Model predicts jump risk premia influencing cryptocurrency futures and option performance.
problem Capturing asymmetric and time-varying skewness in cryptocurrency returns.
method Bivariate Hawkes process with positive and negative jump premia.
result Inferred jump risk premia predict futures cost of carry and option performance.
The paper analyzes implied volatility for European and Asian options under stochastic volatility Bachelier model.
problem Analyzing implied volatility for European and Asian options under stochastic volatility.
method Using Malliavin calculus and anticipating Ito's formula, the paper computes and finds asymptotic formulas for implied volatility and skew.
result The paper provides a short maturity asymptotic formula for the skew of implied volatility that depends on the roughness of the volatility model.
We present extensive evidence that ``risk premium'' is strongly correlated with tail-risk skewness but very little with volatility. We introduce a new, intuitive definition of skewness and elicit an approximately linear relation between the Sharpe ratio of various risk premium strategies (Equity, Fama-French, FX Carry,…
The paper studies estimation of parameters of diffusion market models from historical data. The standard definition of implied volatility for these models presents its value as an implicit function of several parameters, including the risk-free interest rate. In reality, the risk free interest rate is unknown and need …
We revisit the problem of pricing options with historical volatility estimators. We do this in the context of a generalized GARCH model with multiple time scales and asymmetry. It is argued that the reason for the observed volatility risk premium is tail risk aversion. We parametrize such risk aversion in terms of thre…
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 integrated into the theoretical framework of convex monetary measures of risk. In …
The paper develops a new framework for managing asymmetric volatility.
problem Managing asymmetric volatility to improve recovery and participation.
method Path-dependent framework for asymmetric volatility management.
result Skew engineering reduces harmful downside participation more than productive upside participation.
Accumulated stock returns exhibit tempered skew t-distribution.
problem Analyzing the distribution of stock returns over multiple days.
method Employing a tempered skew t-distribution model.
result Tempered skew t-distribution fits the distribution of accumulated stock returns well.
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 options which are written in terms of the implied volatility are given. In particular…
Gaussian copulas are widely used in the industry to correlate two random variables when there is no prior knowledge about the co-dependence between them. The perturbed Gaussian copula approach allows introducing the skew information of both random variables into the co-dependence structure. The analytical expression of…
GG distribution improves option pricing for negatively skewed spot price distributions.
problem Inaccurate Black-Scholes model for negatively skewed spot price distributions.
method Applied Generalized Gamma (GG) distribution as a Risk-Neutral Density (RND) for Heston's SV model.
result GG distribution better matches market option data with negatively skewed spot price distributions.
Markov Chain Monte Carlo is repeatedly used to analyze the properties of intractable distributions in a convenient way. In this paper we derive conditions for geometric ergodicity of a general class of nonparametric stochastic volatility models with skewness driven by hidden Markov Chain with switching.
We revisit the ``Smile Dynamics'' problem, which consists in relating the implied leverage (i.e. the correlation of the at-the-money volatility with the returns of the underlying) and the skew of the option smile. The ratio between these two quantities, called ``Skew-Stickiness Ratio'' (SSR) by Bergomi (Smile Dynamics …
Flexible model captures commodity skews with maturity effects.
problem Capturing market skew in commodity futures with maturity effects.
method Non-parametric extension with leverage functions, calibrated using Monte Carlo simulation.
result Model accurately captures market smile and implied variance accumulation.
The Black-Scholes implied volatility skew at the money of SPX options is known to obey a power law with respect to the time-to-maturity. We construct a model of the underlying asset price process which is dynamically consistent to the power law. The volatility process of the model is driven by a fractional Brownian mot…
A small-time Edgeworth expansion of the density of an asset price is given under a general stochastic volatility model, from which asymptotic expansions of put option prices and at-the-money implied volatilities follow. A limit theorem for at-the-money implied volatility skew and curvature is also given as a corollary.…