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.
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
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.
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).
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.
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.
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.
We undertake a systematic comparison between implied volatility, as represented by VIX (new methodology) and VXO (old methodology), and realized volatility. We compare visually and statistically distributions of realized and implied variance (volatility squared) and study the distribution of their ratio. We find that t…
Large batch sizes reduce gradient variance in DP-SGD, improving privacy.
problem Understanding why large batch sizes work in DP-SGD.
method Decomposed total gradient variance into subsampling and noise-induced variances, proving batch size independence in the limit.
result Large batch sizes reduce effective total gradient variance, improving privacy in DP-SGD.
We study distributions of realized variance (squared realized volatility) and squared implied volatility, as represented by VIX and VXO indices. We find that Generalized Beta distribution provide the best fits. These fits are much more accurate for realized variance than for squared VIX and VXO -- possibly another indi…
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 behaviour at small strikes is uniquely determined by the mass of the atom up to high…
Revisits Lee's Moment Formula, relaxing moment assumptions for implied volatility.
problem Implied volatility constraints under finite log-moments.
method Analyzes stock price martingale with finite log-moments, derives new bounds and proof.
result New bounds on implied volatility growth, relaxes moment assumptions.
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.
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.
We develop a dynamic version of the SSVI parameterisation for the total implied variance, ensuring that European vanilla option prices are martingales, hence preventing the occurrence of arbitrage, both static and dynamic. Insisting on the constraint that the total implied variance needs to be null at the maturity of t…
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.
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.
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.
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 show that in a large class of stochastic volatility models with additional skew-functions (local-stochastic volatility models) the tails of the cumulative distribution of the log-returns behave as exp(-c|y|), where c is a positive constant depending on time and on model parameters. We obtain this estimate proving a …
We consider the class of self-similar Gaussian stochastic volatility models, and compute the small-time (near-maturity) asymptotics for the corresponding asset price density, the call and put pricing functions, and the implied volatilities. Unlike the well-known model-free behavior for extreme-strike asymptotics, small…
We investigate the joint dynamics of spot and implied volatility from an empirical perspective. We focus on the equity market with the SPX Index our underlying of choice. Using only observable quantities, we extract the instantaneous variance curves implied by the market and study their daily variations jointly with sp…
We give a new proof of the representation of implied volatility as a time-average of weighted expectations of local or stochastic volatility. With this proof we clarify the question of existence of 'forward implied variance' in the original derivation of Gatheral, who introduced this representation in his book 'The Vol…
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. Study finds adding more information to robust option pricing does not improve bounds.
problem Exploring robust pricing of financial claims using minimal assumptions.
method Empirical study of variance options, incorporating intermediate market data.
result Incorporating more information does not improve robust pricing bounds.
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 calculates Bachelier option prices using Taylor expansions and applies it as a variance reduction technique.
problem Calculating Bachelier option prices and variance reduction in correlated cases.
method Taylor expansions and classical Itô calculus to derive option prices, uses negative powers of future mean volatility.
result The paper provides a new method to calculate Bachelier option prices and applies it to reduce variance in Monte Carlo simulations.
GCNs improve regression tasks by aggregating neighbor signals.
problem GCNs' statistical properties in regression tasks are poorly understood.
method Examined two GCN convolutions and their impact on learning error.
result GCNs have a bias-variance trade-off that depends on neighborhood size and topology.
We introduce an affine extension of the Heston model where the instantaneous variance process contains a jump part driven by α-stable processes with α∈(1,2]. In this framework, we examine the implied volatility and its asymptotic behaviors for both asset and variance options. Furthermore, we examine the jump clus…
Clustering stocks reduces estimation error in global minimum variance portfolio.
problem High estimation error in covariance matrix estimation.
method Bounded clustering to limit maximum cluster size.
result Reduction in out-of-sample volatility and gap between in-sample and out-of-sample volatility.
The rough Bergomi model, introduced by Bayer, Friz and Gatheral [Quant. Finance 16(6), 887-904, 2016], is one of the recent rough volatility models that are consistent with the stylised fact of implied volatility surfaces being essentially time-invariant, and are able to capture the term structure of skew observed in e…
The paper connects semi-parametric estimates to European option pricing.
problem Estimating European option prices using semi-parametric methods.
method Connecting estimates by de la Peña, Ibragimov and Jordan, Scarf, and Lo.
result The estimates imply European option prices.
We extend the model-free formula of [Fukasawa 2012] for E[Ψ(XT)], where XT=logST/F is the log-price of an asset, to functions Ψ 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…
For any strictly positive martingale S=exp(X) for which X has a characteristic function, we provide an expansion for the implied volatility. This expansion is explicit in the sense that it involves no integrals, but only polynomials in the log strike. We illustrate the versatility of our expansion by computing t…
In this paper, we implement and test two types of market-based models for European-type options, based on the tangent Levy models proposed recently by R. Carmona and S. Nadtochiy. As a result, we obtain a method for generating Monte Carlo samples of future paths of implied volatility surfaces. These paths and the surfa…
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.
A new QHR model extends HR model with a quadratic variance function.
problem Modeling volatility with greater flexibility and stationarity.
method Introducing a quadratic variance function to the HR model, maintaining Markovian property.
result Stationary distribution of the QHR model is Pearson type IV.
Reduces quantifier variance with accuracy optimization of base classifier.
problem Minimizing quantifier variance under prior probability shift.
method Optimizes the Brier score of a base classifier for training data.
result Optimizing Brier score on training data reduces quantifier variance on test data.
Paper provides an explicit formula for local volatility in Cheyette models.
problem Approximating local volatility in Cheyette interest rate models.
method Extended Dupire framework, perturbation methods, probabilistic techniques.
result Explicit analytical formula for local volatility in Cheyette models.
Sharp 2-Wasserstein bounds for DDPMs derived from Föllmer process.
problem Sampling error bounds for DDPMs in 2-Wasserstein distance.
method Lipschitz-type conditions on score function, Föllmer process, and log-concave target distributions.
result Sharp upper bounds for DDPMs in 2-Wasserstein distance, optimal in dimension and steps.
New algorithm reduces regret in infinite MDPs with optimal variance-dependent bounds.
problem Infinite horizon MDPs lack optimal algorithms with low regret.
method Developed a UCB-style algorithm for average-reward and γ-regret.
result Achieved optimal variance-dependent regret bounds for both objectives.
New algorithm reduces optimization complexity in adaptive mirror descent.
problem Optimizing complex, non-smooth, non-convex functions efficiently.
method SVRAMD: Variance Reduced Adaptive Mirror Descent.
result Variance reduction accelerates convergence in adaptive mirror descent.
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.
In this paper, we prove that some Gaussian structural equation models with dependent errors having equal variances are identifiable from their corresponding Gaussian distributions. Specifically, we prove identifiability for the Gaussian structural equation models that can be represented as Andersson-Madigan-Perlman cha…
In the recent years, banks have sold structured products such as worst-of options, Everest and Himalayas, resulting in a short correlation exposure. They have hence become interested in offsetting part of this exposure, namely buying back correlation. Two ways have been proposed for such a strategy : either pure correl…
The paper examines the short-time implied volatility of additive processes and finds key parameters.
problem Characterizing the short-time implied volatility of equity markets.
method Examined pure jump exponential additive processes with power-law scaling parameters.
result The implied volatility is consistent with equity market characteristics if and only if β=1 and δ=-1/2.
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 paper calculates sensitivities for financial derivatives using path weighting methods.
problem Computing sensitivities for path-dependent financial derivatives with high variance and degeneracy issues.
method Proposes explicit path weighting formula, variance reduction adjustment, and covariance inflation technique.
result Effective methods to address high variance and degeneracy in sensitivities computation.