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 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 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.
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…
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.
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.
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.
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…
Approximates bond option volatilities using affine short-rate models.
problem Calculating implied volatilities for bond options.
method Derive asymptotic approximation for bond option volatilities under affine short-rate dynamics.
result Accuracy of approximation validated through numerical experiments.
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.
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.
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.
Low-frequency historical data, high-frequency historical data and option data are three major sources, which can be used to forecast the underlying security's volatility. In this paper, we propose two econometric models, which integrate three information sources. In GARCH-Itô-OI model, we assume that the option-implied…
A new model for pricing ultra-short-term options with complex volatility patterns.
problem Complex pricing of ultra-short-term options due to oscillations in implied volatility.
method Edgeworth++ model with nonparametric stochastic volatility and deterministic shift extension.
result Fast and accurate closed-form option pricing for ultra-short-term options.
Enhanced options trading strategies using advanced portfolio optimization.
problem Generating consistent positive returns in high-frequency options trading.
method Advanced portfolio optimization techniques applied to SPY options data.
result Sophisticated strategies incorporating advanced Greeks show potential in high-frequency trading.
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.
Measures of implied volatility roughness corrected for bias.
problem Bias in measuring implied volatility roughness.
method Examined implied volatility of short-term options and VIX index, corrected for bias.
result Corrected measures indicate appropriate proxies for underlying volatility.
New formula for implied volatility from Black-Scholes model.
problem Computing implied volatility from Black-Scholes model.
method Analytical solution using inverse Gaussian distribution.
result Explicit formulas for implied volatility with high precision.
This study compares SPX and VIX options and quantifies their relationship.
problem Understanding the relationship between SPX and VIX options markets.
method Uses moment formulas in a model-free approach to compare implied volatilities.
result SPX options reflect the extreme-strike asymptotics of VIX options and vice versa.
Study finds a small correction to Asian option volatility.
problem Implied volatility of Asian options at short maturity.
method Large deviations property and asymptotic expansion for the Hartman-Watson distribution.
result Subleading correction to Asian option volatility is derived.
Enhanced hedging for S&P 500 options using volatility surface data.
problem Optimizing hedging strategies for S&P 500 options with transaction costs.
method Deep policy gradient reinforcement learning with volatility surface feedback.
result Outperforms conventional hedging methods in simulations and backtesting.
Proposes deep hedging for index options using implied volatility surface.
problem Managing risk in index option portfolios with complex dynamics.
method Integrates surface-informed decisions with multiple hedging instruments, accounting for transaction costs and variance risk premium.
result Consistently outperforms traditional hedging strategies across various market conditions.
W-shaped vol curves in liquid options can be modeled with two variance-gamma models.
problem Reproducing W-shaped implied volatility curves in liquid option markets.
method Using a mixture of two variance-gamma models.
result W-shaped vol curves can be generated with fewer distributions (two) compared to lognormal models (at least three).
Extracting implied information, like volatility and/or dividend, from observed option prices is a challenging task when dealing with American options, because of the computational costs needed to solve the corresponding mathematical problem many thousands of times. We will employ a data-driven machine learning approach…
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.
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…
We examine the small expiry behaviour of European call options in stock price models of exponential Lévy type. In most cases of interest, we are able to identify the exact small expiry asymptotics. In "complete generality" we are able to show that the time value of the call option has O(τ) decay as τ(time to expiry) go…
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.
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 financialization of futures markets in the early 2000s, we investigate if these extant mod…
We investigate whether it is possible to formulate option pricing and hedging models without using probability. We present a model that is consistent with two notions of volatility: a historical volatility consistent with statistical analysis, and an implied volatility consistent with options priced with the model. The…
The model outperforms other models in option pricing, especially for short-term implied volatility.
problem Improper calibration and pricing of exotic options in financial models.
method Stochastic volatility model with double-exponential jumps, Fourier pricing techniques.
result The model outperforms other models in fitting the short-term implied volatility smile and pricing exotic options.
The paper proposes a new method to calibrate option pricing models that accurately match both volatility surfaces and variance term structures.
problem Calibrated models often produce inaccurate variance term structures relative to market observations.
method The paper introduces a joint calibration framework that augments the conventional objective function with a penalty term for variance term structure deviations, using a hyperparameter to balance volatility surface and variance term structure weights.
result The proposed method accurately fits observed option prices while delivering realistic term structures of variance.
New model prices crypto options by clustering market regimes and using implied volatility.
problem Inaccurate option pricing for volatile crypto markets.
method Time-regime clustering with Implied Stochastic Volatility Model (ISVM).
result MR-ISVM overcomes complexity and adapts to market dynamics.
QLBS and RLOP methods improve option pricing and hedging performance.
problem Improving option pricing and hedging performance under market frictions.
method Incorporates risk aversion and trading costs into QLBS, proposes RLOP approach.
result RLOP outperforms in dynamic hedging by reducing shortfall probability.
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 surface prediction method combining deep learning and attention mechanism is pioneer…
The paper analyzes LETF option markets using moneyness scaling to find statistical arbitrage opportunities.
problem Statistical discrepancies between levered and unlevered ETF option implied volatility smiles.
method Bootstrap uniform confidence bands, dynamic semiparametric factor model, moneyness scaling, Heston stochastic volatility.
result Trading opportunities exist on LETF market, and a statistical arbitrage strategy generates positive returns.
Breaks circular dependency in synthetic option pricing with a novel model.
problem Circular dependency in implied volatility limits synthetic data for machine learning and risk analysis.
method Uses a Jump-Hidden Markov Model to generate price paths and a modified Heston process to convert paths into implied volatility.
result Framework generates realistic synthetic American option prices without external calibration.
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…
Extends pricing methods for index options under rough volatility.
problem Pricing and hedging of index options under non-Markovian dynamics.
method Extension of large deviations methods to non-local volatility dynamics, specifically rough volatility.
result Validates the approach for pricing index options under rough 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 this article, we look at the effect of volatility clustering on the risk indifference price of options described by Sircar and Sturm in their paper (Sircar, R., & Sturm, S. (2012). From smile asymptotics to market risk measures. Mathematical Finance. Advance online publication. doi:10.1111/mafi.12015). The indiffere…
Study leading-order asymptotics for VIX option prices in Bergomi models.
problem Understanding VIX option pricing in Bergomi models.
method Analytical approach to derive leading-order asymptotics for VIX option prices in Bergomi models.
result Closed-form solutions for VIX option prices in Bergomi models are derived.
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…
The paper provides formulas for volatility in various models, including rough volatility.
problem Calibrating SPX and VIX options with rough volatility models.
method Developed explicit formulae using Malliavin calculus for Gaussian processes.
result New insights on joint calibration of SPX and VIX options.
In this paper new analytical and numerical approaches to valuating path-dependent options of European type have been developed. The model of stochastic volatility as a basic model has been chosen. For European options we could improve the path integral method, proposed B. Baaquie, and generalized it to the case of path…
We formulate and analyze an inverse problem using derivatives prices to obtain an implied filtering density on volatility's hidden state. Stochastic volatility is the unobserved state in a hidden Markov model (HMM) and can be tracked using Bayesian filtering. However, derivative data can be considered as conditional ex…
Study uses SABR model to create implied volatilities from sparse quotes.
problem Creating accurate implied volatility surfaces from limited market data.
method Multitask Gaussian process with SABR model embeddings and hierarchical regularization.
result Model produces more accurate volatilities than single-task methods.
The literature on volatility modelling and option pricing is a large and diverse area due to its importance and applications. This paper provides a review of the most significant volatility models and option pricing methods, beginning with constant volatility models up to stochastic volatility. We also survey less comm…