Extends Heston model with local volatility for better fit to market volatilities.
problem Fitting stochastic volatility models to market volatilities.
method Adds local volatility term to rough-Heston model, preserving stylized results.
result Provides a proper extrapolation scheme for calibration.
We consider an asset whose risk-neutral dynamics are described by a general class of local-stochastic volatility models and derive a family of asymptotic expansions for European-style option prices and implied volatilities. Our implied volatility expansions are explicit; they do not require any special functions nor do…
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).
We study the local volatility function in the Foreign Exchange market where both domestic and foreign interest rates are stochastic. This model is suitable to price long-dated FX derivatives. We derive the local volatility function and obtain several results that can be used for the calibration of this local volatility…
New model shows VIX futures are more expensive than local volatility model suggests.
problem VIX futures pricing under local volatility model is incorrect.
method Developed a continuous stochastic volatility model to show VIX futures are more expensive than local volatility model.
result Inversion of convex ordering between local and stochastic variances observed in SPX market for short maturities.
In this paper, we study the price of Variable Annuity Guarantees, especially of Guaranteed Annuity Options (GAO) and Guaranteed Minimum Income Benefit (GMIB), and this in the settings of a derivative pricing model where the underlying spot (the fund) is locally governed by a geometric Brownian motion with local volatil…
Derives short-term option pricing asymptotics in local-stochastic volatility models.
problem Short-term option pricing in local-stochastic volatility models.
method Large deviations theory and variational methods.
result Explicit series expansions for implied volatility and asymptotic results for European and VIX options.
LOV model calibrates European and American options with path-dependent volatility.
problem Calibrating European and American options with path-dependent volatility.
method Designing a local volatility model that incorporates path-dependent shocks through an occupation sensitivity function.
result LOV model successfully calibrates options chains with automatic European vanilla option calibration and path-dependent flexibility.
New method calibrates local volatility models to marginal distributions.
problem Calibrating local volatility models to specific marginal distributions.
method Inspired by volatility interpolation, constructs time-homogeneous or continuous local volatility functions.
result Efficient numerical algorithms for constructing local volatility functions.
Proposes new Monte Carlo methods for calibrating local volatility models with stochastic components.
problem Calibrating local volatility models with stochastic drift and diffusion.
method Developed Monte Carlo algorithms for three models: local volatility with stochastic interest rates, stochastic local volatility with deterministic interest rates, and stochastic local volatility with stochastic interest rates.
result Conditions for the existence of local volatility given European option prices, stochastic interest rate model parameters, and correlations.
Paper approximates rough stochastic local volatility models for efficient computation.
problem No unified method for rough stochastic local volatility models.
method Semimartingale and continuous-time Markov chain approximation.
result Fast CTMC algorithm with weak convergence proved.
Paper improves stochastic collocation for local volatility models.
problem Improving local volatility models for assets with boundaries.
method Applied stochastic collocation to lognormal distributions, derived analytical local volatility.
result Simple analytical Dupire local volatility derived from option prices.
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. …
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.
The article reviews how to set stochastic volatility model parameters.
problem Choosing parameters for stochastic volatility models.
method Examines existing literature on various methods.
result Different approaches to setting stochastic volatility 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.
Study compares MC and QMC methods for pricing and risk analysis in a hyperbolic local volatility model.
problem Derivative pricing and risk analysis in a hyperbolic local volatility model.
method Application of Monte Carlo and Quasi Monte Carlo methods for pricing and risk analysis.
result Quasi Monte Carlo methods show superior performance in high-dimensional integration for derivative pricing and risk analysis.
A new method to estimate local volatility from high-frequency data.
problem Quantitative trading risk management needs a better way to estimate volatility.
method Realized local volatility surface estimated via high-frequency data and Bayesian nonparametric estimation.
result The method can capture counterfactual volatility and improve risk management.
Existence of calibrated local stochastic volatility models proven for non-regular coefficients.
problem Existence of calibrated local stochastic volatility models in finance.
method Investigation of McKean--Vlasov equations with minimal continuity assumptions on coefficients, providing existence and propagation of chaos results.
result Existence of calibrated local stochastic volatility models for appropriate stochastic volatility parameters.
A robust implementation of a Dupire type local volatility model is an important issue for every option trading floor. Typically, this (inverse) problem is solved in a two step procedure : (i) a smooth parametrization of the implied volatility surface; (ii) computation of the local volatility based on the resulting call…
The Local Volatility model is a well-known extension of the Black-Scholes constant volatility model whereby the volatility is dependent on both time and the underlying asset. This model can be calibrated to provide a perfect fit to a wide range of implied volatility surfaces. The model is easy to calibrate and still ve…
Proves existence and uniqueness of calibrated LSV model.
problem Calibrating a local stochastic volatility model to market data.
method Proves strong existence and uniqueness of solution to a McKean-Vlasov SDE.
result Establishes well-posedness of a calibrated two-factor LSV model.
The Bass model is calibrated to vanilla options using a fixed-point equation.
problem Calibration of the Bass local volatility model to vanilla options.
method Solving a fixed-point equation to achieve calibration.
result Existence and uniqueness of the solution to the fixed-point equation, and linear convergence of the fixed-point iteration scheme.
Motivated by marginals-mimicking results for Itô processes via SDEs and by their applications to volatility modeling in finance, we discuss the weak convergence of the law of a hypoelliptic diffusions conditioned to belong to a target affine subspace at final time, namely L(Zt∣Yt=y) if $X_{\cdot}=(Y_\cd…
We introduce a new class of local volatility models. Within this framework, we obtain expressions for both (i) the price of any European option and (ii) the induced implied volatility smile. As an illustration of our framework, we perform specific pricing and implied volatility computations for a CEV-like example. Nume…
We discuss the possibility of obtaining model-free bounds on volatility derivatives, given present market data in the form of a calibrated local volatility model. A counter-example to a wide-spread conjecture is given.
Two ML approaches learn local volatility surfaces from option prices, with GP being arbitrage-free.
problem Interpolating European vanilla option prices to create a local volatility surface.
method Gaussian process regression and neural net with arbitrage penalties.
result GP approach is arbitrage-free and yields best out-of-sample calibration error.
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…
Asymptotic analysis of short-maturity options on realized variance in local-stochastic volatility models.
problem Analyzing the behavior of short-maturity options on realized variance in local-stochastic volatility models.
method Large deviations theory and variational problems to solve rate functions for different cases.
result Explicit solutions for the rate function in the uncorrelated case and upper/lower bounds and expansions for the correlated case.
The paper analyzes Asian options in local volatility models at short maturity.
problem Short-maturity pricing and hedging of Asian options in local volatility models.
method Approximation of local volatility model by Gaussian process at short maturity, combined with Malliavin calculus.
result Short-maturity Asian option prices and delta values approximate European counterparts with a specific volatility function.
Improved LV model for interest rate swaptions and caplets.
problem Calibration of arbitrage-free LV models to European options.
method HJM interest rate model with Small Volatility Approximation.
result Deterministic and fast method with excellent calibration accuracy.
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.
We tackle the calibration of the so-called Stochastic-Local Volatility (SLV) model. This is the class of financial models that combines the local and stochastic volatility features and has been subject of the attention by many researchers recently. More precisely, given a local volatility surface and a choice of stocha…
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.
We propose two main applications of Gyöngy (1986)'s construction of inhomogeneous Markovian stochastic differential equations that mimick the one-dimensional marginals of continuous Itô processes. Firstly, we prove Dupire (1994) and Derman and Kani (1994)'s result. We then present Bessel-based stochastic volatility mod…
Bayesian method calibrates local volatility with Gaussian processes.
problem Calibrating local volatility models is challenging.
method Bayesian inference with Gaussian process priors.
result Rich probabilistic model of local volatility with uncertainty.
We consider a stochastic volatility model where the moment generating function of the logarithmic price is finite only on part of the real line. Using a new Tauberian result obtained in [1] and [2], we show that the knowledge of the moment generating function near its critical moment gives a sharp asymptotic expansion …
Study short-maturity Asian option pricing in LSV models using large deviations theory.
problem Derive short-maturity asymptotics for Asian option prices in LSV models.
method Large deviations theory and novel expansion method.
result Explicit series expansions for the solution of the variational problem around the ATM point.
Proposes a calibration method for various volatility models.
problem Calibrating local-stochastic and path-dependent volatility models to options.
method Generic calibration framework using forward PIDE and particle method.
result Calibration well within market no-touch bid--ask range.
Efficient method for pricing multi-asset options with local volatility.
problem Pricing options on multiple assets with varying volatility.
method Generic hybrid numerical method for efficient pricing.
result Efficient pricing of multi-asset options with local volatility.
By Gyongy's theorem, a local and stochastic volatility (LSV) model is calibrated to the market prices of all European call options with positive maturities and strikes if its local volatility function is equal to the ratio of the Dupire local volatility function over the root conditional mean square of the stochastic v…
Quantum algorithm for multi-asset option pricing under different volatility models.
problem Efficiently pricing multi-asset options under various volatility models using quantum computing.
method Developed an end-to-end quantum PDE framework for European option pricing, solving PDEs after discretization on spatial grids.
result Quantum framework provides polynomial improvement in resource usage compared to classical methods.
New approach improves computational efficiency of Bass Local Volatility model.
problem Eliminate interpolation and improve computational efficiency in local volatility models.
method Combines local quadratic estimation and lognormal mixture tails for state price densities; uses trapezoidal rule for numerical convolutions.
result Proposed method outperforms traditional numerical methods in option pricing and market case studies.
Study improves caplet calibration for 1Y maturity using different models.
problem Calibrate 1Y caplet smile better across strike range.
method Alternative local volatility terms and stochastic volatility models.
result Some models calibrate well to 1Y caplet smile across strike range.
We introduce a new factor model for log volatilities that performs dimensionality reduction and considers contributions globally through the market, and locally through cluster structure and their interactions. We do not assume a-priori the number of clusters in the data, instead using the Directed Bubble Hierarchical …
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.
The study calibrates VIX and VXX options using a multi-factor model.
problem Calibration failure of VIX and VXX options using stochastic or local volatility models.
method Presented a multi-factor stochastic-local volatility model.
result Joint calibration of VIX and VXX options successfully achieved.
It is well known that in models with time-homogeneous local volatility functions and constant interest and dividend rates, the European Put prices are transformed into European Call prices by the simultaneous exchanges of the interest and dividend rates and of the strike and spot price of the underlying. This paper inv…