We study the dynamics of the normal implied volatility in a local volatility model, using a small-time expansion in powers of maturity T. At leading order in this expansion, the asymptotics of the normal implied volatility is similar, up to a different definition of the moneyness, to that of the log-normal volatility. …
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48 results for “Normal volatilities”
Monotonicity of normalized implied-volatility coordinates under no-arbitrage
problem Monotonicity of normalized implied-volatility coordinates under no-arbitrage
method Elementary discrete no-arbitrage proof
result Monotonicity principle extended to Bachelier implied volatility
Two new rational formulae for normal implied volatility are presented.
problem Calculating normal implied volatility using iterative methods.
method Two explicit rational formulae that avoid iteration and logarithms.
result Accurate and fast formulae for normal implied volatility.
First, we show that implied normal volatility is intimately linked with the incomplete Gamma function. Then, we deduce an expansion on implied normal volatility in terms of the time-value of a European call option. Then, we formulate an equivalence between the implied normal volatility and the lognormal implied volatil…
Modified Vanna-Volga method constructs Normal volatility smiles.
problem No method existed for constructing Normal volatility smiles.
method Modified Vanna-Volga method applied to Normal volatilities.
result The Vanna-Volga method can easily fit both convex and concave smiles.
Establishes a microstructural foundation for a rough log-normal volatility model.
problem Developing a robust model for financial volatility under microstructural effects.
method Introduced a sequence of order-driven financial market models with Poisson process arrivals and analyzed their convergence to a log-normal rough volatility model.
result Weak convergence of price-volatility process to a log-normal rough volatility model with established weak error rates.
The paper calculates option prices for assets with stochastic volatility using FFT.
problem Calculating option prices for assets with stochastic volatility.
method Assumed normal asset dynamics with stochastic volatility following CIR process. Used FFT for evaluation and compared with Monte Carlo simulation.
result Comparison of FFT and Monte Carlo results for option pricing.
We propose a novel time discretization for the log-normal SABR model and derive its asymptotic properties.
problem Analyzing the log-normal SABR model's time-discretized behavior and implied volatility surface.
method We use the Euler-Maruyama scheme for time discretization and derive asymptotic properties in the limit of large number of time steps.
result We derive an exact representation of the implied volatility surface for arbitrary maturity and strike in the asymptotic regime.
We consider an interest rate model with log-normally distributed rates in the terminal measure in discrete time. Such models are used in financial practice as parametric versions of the Markov functional model, or as approximations to the log-normal Libor market model. We show that the model has two distinct regimes, a…
We discuss the class of "Quadratic Normal Volatility" models, which have drawn much attention in the financial industry due to their analytic tractability and flexibility. We characterize these models as the ones that can be obtained from stopped Brownian motion by a simple transformation and a change of measure that o…
In this paper we investigate general linear stochastic volatility models with correlated Brownian noises. In such models the asset price satisfies a linear SDE with coefficient of linearity being the volatility process. This class contains among others Black-Scholes model, a log-normal stochastic volatility model and H…
Critical volatility triggers log-normal to power-law transitions in interconnected systems.
problem Understanding the transition from log-normal to power-law distributions in interconnected systems.
method Analyzing an infinite option-on-option chain model, deriving a critical volatility threshold.
result A critical volatility threshold of approximately 250.66% for unconditional cases, dropping to 125.3% with selective survival.
Study on estimating volatility of volatility using Fourier methods and provides insights into volatility dynamics.
problem Estimating the volatility of volatility (vol-of-vol) accurately and efficiently.
method Used Fourier methodology to estimate integrated volatility of volatility, bias-corrected and without bias-correction, comparing their asymptotic properties and accuracy.
result The bias-corrected estimator reaches the optimal rate , while the uncorrected estimator has a slower rate and smaller asymptotic variance.
We study the pricing problem for a European call option when the volatility of the underlying asset is random and follows the exponential Ornstein-Uhlenbeck model. The random diffusion model proposed is a two-dimensional market process that takes a log-Brownian motion to describe price dynamics and an Ornstein-Uhlenbec…
We calculate realized volatility of the Nikkei Stock Average (Nikkei225) Index on the Tokyo Stock Exchange and investigate the return dynamics. To avoid the bias on the realized volatility from the non-trading hours issue we calculate realized volatility separately in the two trading sessions, i.e. morning and afternoo…
The study explains how market-makers' hedging affects stock volatility during gamma-squeeze events.
problem Endogenous volatility amplification in option markets during gamma-squeeze events.
method Developed a theoretical framework linking hedging behavior and market turbulence, incorporating beta-normalized volatility.
result Low-beta stocks amplify volatility more during gamma-squeeze events.
Develops a martingale expansion for stochastic volatility models.
problem Approximating marginal distributions of stochastic volatility models.
method Martingale expansion framework for continuous stochastic volatility models.
result First-order perturbation expansions for small volatility-of-volatility and fast mean-reversion models.
Study proposes a new volatility model for option pricing with heavy-tailed distributions.
problem Developing a volatility model for accurate option pricing with heavy-tailed distributions.
method A one-parameter extension of the normal SABR model based on arithmetic Brownian motion, using generalized Bougerol's identities.
result The proposed model has a closed-form Monte-Carlo simulation scheme and follows Johnson's distribution.
Extreme times for volatility processesphysics.soc-ph
We present a detailed study on the mean first-passage time of volatility processes. We analyze the theoretical expressions based on the most common stochastic volatility models along with empirical results extracted from daily data of major financial indices. We find in all these data sets a very similar behavior that …
Representation of probability distributions with implied volatility and biological rationaleq-fin.ST
Proposes a new way to represent uncertainty using implied volatility.
problem Uncertainty in financial markets and biological systems.
method Mathematical analysis of various probability distributions.
result Representation of different probability distributions using BSM implied volatility.
Volatility distribution in the S&P500 Stock Indexcond-mat.stat-mech
We study the volatility of the S&P500 stock index from 1984 to 1996 and find that the volatility distribution can be very well described by a log-normal function. Further, using detrended fluctuation analysis we show that the volatility is power-law correlated with Hurst exponent .
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…
This paper examines Bachelier implied volatility at extreme strikes.
problem Investigates appropriate implied volatility extrapolation at extreme strikes.
method Compares Bachelier and Black-Scholes models, focusing on normal distribution and vanilla options.
result Bachelier implied variance grows at most linearly in log-moneyness, similar to Black-Scholes.
ReVol normalizes stock price features to mitigate distribution shifts, improving prediction accuracy.
problem Distribution shifts in stock price data hinder accurate prediction.
method ReVol uses normalization, attention-based estimation, and geometric Brownian motion.
result ReVol achieves an average improvement of more than 0.03 in IC and over 0.7 in SR.
We derive the exact solution of a one-dimensional Markov functional model with log-normally distributed interest rates in discrete time. The model is shown to have two distinct limiting states, corresponding to small and asymptotically large volatilities, respectively. These volatility regimes are separated by a phase …
We add size factor to CAPM and normalize residuals by Volatility Index.
problem Capturing the size effect in CAPM and making residuals Gaussian.
method Insert size effect, normalize residuals by Volatility Index, and fit model to real-world data.
result The new model shows long-term stability and connects to Stochastic Portfolio Theory.
We extend the model-free formula of [Fukasawa 2012] for , where is the log-price of an asset, to functions of exponential growth. The resulting integral representation is written in terms of normalized implied volatilities. Just as Fukasawa's work provides rigourous ground for Ch…
We solve the escape problem for the Heston random diffusion model. We obtain exact expressions for the survival probability (which ammounts to solving the complete escape problem) as well as for the mean exit time. We also average the volatility in order to work out the problem for the return alone regardless volatilit…
Develops a GMM method to estimate roughness in stochastic volatility models.
problem Estimating roughness in stochastic volatility models with fractional Brownian motion.
method GMM approach for log-normal models with integrated variance and noisy realized variance.
result Consistent and asymptotically normal parameter estimator with bias correction.
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.
Stochastic Volatility in Mean models with heavy-tailed distributions using Hidden Markov Models
problem Accurate inference for Stochastic Volatility in Mean models with heavy-tailed distributions
method Numerically stable estimation procedure and parallel computing
result Significant reduction in computational times
A rough SABR formulaq-fin.MF
Derives a rough SABR formula for short maturities.
problem Modeling volatility smiles under rough volatility.
method Derives an ODE and solves it numerically.
result Develops a very accurate approximation called the rough SABR formula.
Using classical Taylor series techniques, we develop a unified approach to pricing and implied volatility for European-style options in a general local-stochastic volatility setting. Our price approximations require only a normal CDF and our implied volatility approximations are fully explicit (ie, they require no spec…
The tGARCH-NIG model best estimates Bitcoin volatility.
problem Estimating volatility of Bitcoin with skewed and leptokurtic distributions.
method Three GARCH models (sGARCH, iGARCH, tGARCH) with different distributions.
result tGARCH-NIG model best captures Bitcoin volatility.
A new fast method simulates stochastic volatility models.
problem Simulating stochastic volatility models efficiently.
method Karhunen-Loève expansions to express stochastic volatility as sine series, followed by analytical derivation of integrals.
result Simulation is several hundred times faster than existing methods.
Study on Kyle's model with stochastic liquidity impacts asset volatility.
problem Impact of stochastic volatility of noise trading on asset volatility.
method Construct equilibrium for continuous-time Kyle's model with stochastic liquidity.
result In equilibrium, Kyle's Lambda and its inverse are submartingales.
A multi-time scale non-Gaussian model of stock returnscond-mat.other
We propose a stochastic process for stock movements that, with just one source of Brownian noise, has an instantaneous volatility that rises from a type of statistical feedback across many time scales. This results in a stationary non-Gaussian process which captures many features observed in time series of real stock r…
Paper develops a new estimator for rough volatility parameters.
problem Estimating rough volatility parameters from high-frequency data.
method Develops a semiparametric estimator for in rough volatility models.
result The estimator achieves optimal convergence rate in minimax sense.
We calculate the realized volatility in the spin model of financial markets and examine the returns standardized by the realized volatility. We find that moments of the standardized returns agree with the theoretical values of standard normal variables. This is the first evidence that the return dynamics of the spin fi…
The study identifies and analyzes different market regimes in equity markets using advanced signal processing techniques.
problem Understanding and quantifying the dynamics of different market regimes in equity markets.
method Data-driven Hilbert--Huang Transform for regime identification, Holo--Hilbert Spectral Analysis for profiling, and Variable-Length Markov Chains for return dynamics modeling.
result Developed markets normalize more effectively as stress subsides, while developing markets retain residual tail dependence and downside persistence.
We prove that Student's t-distribution provides one of the better fits to returns of S&P component stocks and the generalized inverse gamma distribution best fits VIX and VXO volatility data. We further argue that a more accurate measure of the volatility may be possible based on the fact that stock returns can be unde…
Bayesian models improve cryptocurrency forecasting accuracy.
problem Improving cryptocurrency forecasting accuracy using Bayesian models.
method Compared Bayesian models with constant and time-varying volatility, including stochastic volatility and GARCH models.
result Stochastic volatility significantly outperforms VAR in both point and density forecasting.
The paper estimates CoVaR with various models for financial risk analysis.
problem Estimating conditional value-at-risk with financial time series data.
method Fitting multivariate parametric models and copula functions to capture stylized facts of equity returns.
result Backtesting shows that certain models provide better risk estimates than others.
Introduces new financial models using subordinated processes.
problem Modeling asset returns with behavioral finance considerations.
method Introduces multiple internally embedded financial time-clocks, subordinated to Brownian motion, with a behavioral subordinator.
result New log-price process with multiple embedded subordinations, requiring estimation of new parameters.
This paper explores the harmonic mean of implied volatility and its relation to local volatility.
problem Understanding the relationship between implied volatility and local volatility.
method Investigates the harmonic mean of a positive function for any fixed maturity, linking it to Fukasawa's invertible map.
result The short-dated implied volatility approaches the arithmetic mean of the local volatility in a new coordinate system.
Pricing options on illiquid assets using liquid market benchmarks: an application to energy marketsq-fin.CP
The paper models Gasoil options using Brent benchmarks, improving volatility estimation.
problem Inability to directly model illiquid Gasoil options market.
method Jointly models Brent and Gasoil futures prices with a correlated Bachelier model, estimating volatility spread.
result The proposed framework accurately maps Brent implied volatilities to Gasoil implied volatilities.
A spin model is used for simulations of financial markets. To determine return volatility in the spin financial market we use the GARCH model often used for volatility estimation in empirical finance. We apply the Bayesian inference performed by the Markov Chain Monte Carlo method to the parameter estimation of the GAR…
In this paper we study the volatility and its probability distribution function for the cumulative production based on the experience curve hypothesis. This work presents a generalization of the study of volatility in [1], which addressed the effects of normally distributed noise in the production process. Due to its w…