This paper provides a neural approach to represent option implied information.
problem Link between implied density and volatility for arbitrage-free modeling.
method Minimalist perspective on implied volatility, neural representation with arbitrage constraints.
result Shallow feedforward network with a single hidden layer effectively approximates implied density and volatility.
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.
Exact relationships found between ATM slope, volatility swap, and zero vanna.
problem Understanding relationships between implied volatilities and swaps.
method Analyzes exact relationships between ATM slope, volatility swap, and zero vanna.
result Exact relationships between ATM slope, volatility swap, and zero vanna.
Machine learning approximates implied volatility and dividend yield for American options.
problem Challenges in extracting implied information from American options due to computational costs.
method Employing a data-driven machine learning approach, specifically a Calibration Neural Network (CaNN), to estimate implied volatility and dividend yield efficiently.
result Machine learning can be used to estimate implied volatility and dividend yield for American options efficiently.
A new method calculates implied volatilities without using option prices.
problem Calculating implied volatilities without option prices.
method Conic finance approach to uniquely strip volatilities from bid and ask quotes.
result Allows joint calculation of implied liquidity from bid and ask quotes.
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.
Study uses sentiment analysis to predict implied volatility surface, improving prediction accuracy.
problem Improving prediction accuracy of implied volatility surface.
method Constructed daily high-frequency sentiment data, used VAR method, deep learning (BERT, LSTM), FFT, EMD for sentiment decomposition.
result High-frequency sentiment correlates with ATM options' implied volatility, low-frequency with DOTM options.
In informationally efficient financial markets, option prices and this implied volatility should immediately be adjusted to new information that arrives along with a jump in underlying's return, whereas gradual changes in implied volatility would indicate market inefficiency. Using minute-by-minute data on S&P 500 inde…
New FX option interpolations impact implied volatilities.
problem Different interpolations of FX option quotes lead to varying implied volatilities.
method Analysis of various exact interpolations of broker quotes.
result Different interpolations result in different implied volatilities.
Study on implied certainty equivalent rates in financial markets and electric vehicles.
problem Investment risk in financial markets.
method Mathematical derivation of implied certainty equivalent rate, empirical analysis of stock and option data.
result Positive implied certainty equivalent rates are more suitable for investment than negative ones, but higher values increase risk.
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…
Develops a dynamic SSVI model to prevent arbitrage and implied volatility bubbles.
problem Preventing arbitrage in implied volatility models.
method Dynamic SSVI parameterization ensuring European vanilla option prices are martingales.
result No model allows for arbitrage-free implied volatility bubbles.
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…
We use life annuity prices to extract information about human longevity using a framework that links the term structure of mortality and interest rates. We invert the model and perform nonlinear least squares to obtain implied longevity forecasts. Methodologically, we assume a Cox-Ingersoll-Ross (CIR) model for the und…
This study interprets AMM fees as implied volatility, validating their relevance in digital asset markets.
problem Understanding the volatility of fees in decentralized exchange systems.
method Reinterpreting AMM fees as implied volatility and applying fixed-for-floating swaps to quote and validate these volatilities.
result The implied volatilities of digital assets can be accurately quoted using AMM fees, validating the approach.
Study forecasts commodity options' implied volatility using Nelson-Siegel factors.
problem Predicting implied volatility in commodity markets.
method Rolling out-of-sample forecasting with Nelson-Siegel factors.
result Nelson-Siegel factors improve forecasting accuracy for energy and precious metals options.
Symbolic regression finds simple formulas for implied volatility.
problem Discovering accurate parametric representations for implied volatility.
method Symbolic regression to find analytic formulas from market data.
result Symbolic regression identifies compact parametrizations with competitive fitting performance.
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 …
New framework improves option pricing models by addressing volatility dynamics.
problem Challenges in standard option pricing models, especially in deriving implied volatility.
method Developed a new framework called Implied Remaining Variance (IRV), identifying minimal conditions for absence of arbitrage.
result Reformulated results of Schweizer and Wissel (2008b) and independently derived El Amrani, Jacquier and Martini (2021) results within IRV framework.
Paper estimates Hurst parameter from implied volatilities.
problem Estimating Hurst parameter from implied volatilities.
method Uses covariance between asset return and realized volatility, and applies limit theorems for stochastic volatility models.
result Direct relation between covariance and slope of at-the-money implied volatility established.
No-arbitrage constraints on implied variance slope are weak, leading to almost guaranteed arbitrage in many cases.
problem Weak constraints on implied variance slope in the Black-Scholes model lead to arbitrage opportunities.
method Analysis of constraints on implied variance slope and their implications for arbitrage.
result Arbitrage is almost always guaranteed in a wide range of slope values where constraints are enforced.
It is "well known" that there is no explicit expression for the Black-Scholes implied volatility. We prove that, as a function of underlying, strike, and call price, implied volatility does not belong to the class of D-finite functions. This does not rule out all explicit expressions, but shows that implied volatility …
The BBF, SABR, and rough SABR formulas provide nearly arbitrage-free implied vol approximations.
problem Arbitrage in implied volatility calculations.
method Analytical proofs for BBF, SABR, and rough SABR formulas under specific models.
result These formulas offer asymptotically arbitrage-free approximations of implied volatility.
We create precise formulas for VIX option implied volatility.
problem Calibrating VIX option prices in forward variance models.
method Developed closed-form expansions using weak-approximation techniques.
result Explicit formulas for implied volatility with computable correction terms.
Framework predicts implied volatility surface without arbitrage.
problem Predicting implied volatility surface without static arbitrage.
method Two-step framework: feature selection and deep neural network (DNN) construction.
result DNN model for surface construction removes static arbitrage and reduces prediction error.
Calibrates historical and implied correlations in energy markets.
problem Challenges in aligning historical correlations of futures contracts with implied volatility smiles.
method Multiplicative multi-factor Heath-Jarrow-Morton model combined with stochastic volatility from lifted Heston model, using Kemna-Vorst approximation and Fourier-based techniques.
result Remarkable joint historical and implied calibration fits on the German power market.
Paper derives formulas for volatility swap strike and zero vanna implied volatility.
problem Relationship between volatility swap strike and zero vanna implied volatility.
method Applied Malliavin calculus to derive exact formulas.
result Zero vanna implied volatility is a better approximation for volatility swap strike.
PCA reveals a market factor in S&P500 implied volatilities.
problem Constructing factor models from implied volatility data.
method PCA on implied volatility tensor structure.
result An OI and Vega-weighted index is a significant factor.
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.
This paper improves dynamic hedging accuracy using genetic programming to forecast implied volatilities.
problem Improving the accuracy of dynamic hedging using implied volatilities.
method The paper uses genetic programming to forecast implied volatilities and tests the performance of these forecasts in dynamic hedging strategies.
result Genetic programming-generated implied volatilities improve hedging accuracy compared to static training methods.
New model predicts implied volatility using past asset price paths.
problem Forecasting implied volatility surfaces and asset prices.
method Proposes a new model using past asset price trajectories to predict implied volatility.
result Large part of implied volatility movements can be explained by past returns and squares.
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.
Study examines implied volatility behavior in Bachelier model.
problem Characterizing implied volatility in Bachelier model for large strikes.
method Exploiting regular variation theory, derived explicit expressions for Bachelier implied volatility.
result Established a rigorous connection between characteristic function analyticity and volatility smile asymptotic slope.
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…
We derive the implied volatility estimation formula in European power call options pricing, where the payoff functions are in the form of V=(STα−K)+ and V=(STα−Kα)+ (α>0)respectively. Using quadratic Taylor approximations, We develop the computing formula of implied volatility in European power call op…
A new measure, the implied Sharpe ratio, helps investors choose among European options.
problem No concise measure exists to compare different European options.
method Taylor series expansion of state-dependent coefficients in a nonlinear PDE.
result The option with the highest implied Sharpe ratio improves utility the most.
Tutorial on estimating SVM class probabilities.
problem Estimating class probabilities for SVM models.
method Compute implied posterior probabilities via isotonic regression.
result Calibrated implied posterior probabilities for SVMs.
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.
Study on distributions of realized and implied volatility, using Generalized Beta distribution.
problem Understanding the differences and relationships between realized and implied volatility distributions.
method Used Generalized Beta distribution to fit distributions of realized variance and implied volatility (VIX, VXO). Analyzed differences and correlations.
result Generalized Beta distribution provides the best fit for realized variance but not for implied volatility indices (VIX, VXO).
The implied volatility is a crucial element of any financial toolbox, since it is used for quoting and the hedging of options as well as for model calibration. In contrast to the Black-Scholes formula its inverse, the implied volatility, is not explicitly available and numerical approximation is required. We propose a …
We consider implied volatilities in asset pricing models, where the discounted underlying is a strict local martingale under the pricing measure. Our main result gives an asymptotic expansion of the right wing of the implied volatility smile and shows that the strict local martingale property can be determined from thi…
The study analyzes the differences between physical and risk-neutral correlation estimates for equity baskets.
problem Analyzing the differences between physical and risk-neutral correlation estimates for equity baskets.
method Assumed equicorrelation, reduced dimensionality, approximated ICS from implied volatilities, analyzed dynamics using dynamic semiparametric factor model.
result Proposed profitability improvement schemes based on implied correlation forecasts.
We present an Hilbert space formulation for a set of implied volatility models introduced in \cite{BraceGoldys01} in which the authors studied conditions for a family of European call options, varying the maturing time and the strike price T an K, to be arbitrage free. The arbitrage free conditions give a system of…
New method improves accuracy in computing implied volatility.
problem Computing implied volatility from the Black-Scholes model.
method Adaptive gradient descent optimizers for numerical computation.
result More accurate results compared to close form approximation and Newton-Raphson method.
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 tail-wing formulas due to Benaim and Friz. In addition, we analyze Pareto-type tails o…
The growth of the exhange-traded fund (ETF) industry has given rise to the trading of options written on ETFs and their leveraged counterparts {(LETFs)}. We study the relationship between the ETF and LETF implied volatility surfaces when the underlying ETF is modeled by a general class of local-stochastic volatility mo…
Study integrates implied Hurst exponent into IV models for better market efficiency.
problem Capturing market efficiency in IV models based on moneyness.
method Developed an IV model integrating implied Hurst exponent H, optimizing across multiple indexes.
result Model outperforms SABR and fSABR in accuracy, capturing IV-H dynamics.
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.