Derives variance kernel for reaction boundary in financial models.
problem Separating components in financial volatility models.
method Operational-time variance kernel, damped Abel response kernel, closed asymptotic form.
result Operational variance has a closed asymptotic form involving various parameters.
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).
Long maturity options or a wide class of hybrid products are evaluated using a local volatility type modelling for the asset price S(t) with a stochastic interest rate r(t). The calibration of the local volatility function is usually time-consuming because of the multi-dimensional nature of the problem. In this paper, …
Derives operational-time variance kernel for reaction boundaries in financial markets.
problem Separating components in volatility models to better understand market dynamics.
method Derives a variance kernel for a latent-order-book reaction boundary, separating structural boundary cumulant, clock projection, and pricing-measure choice.
result Operational variance has a closed asymptotic form for long-memory forcing, with effective signed-forcing intensity and resilience.
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…
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.
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.
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.
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.
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.
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.
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.
Develops a deep learning method for enforcing no-arbitrage in local volatility surfaces.
problem No-arbitrage conditions not enforced in deep learning approaches for local volatility.
method Jointly interpolates European vanilla option prices, enforcing no-arbitrage through modified loss functions or network architectures.
result Demonstrates the effectiveness of enforcing no-arbitrage in local volatility surfaces using deep learning.
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…
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.
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.
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.
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.
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…
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.
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.
New algorithm calibrates local volatility from option prices using deep neural networks.
problem Calibrating local volatility from market option prices with reduced interpolation and reprice errors.
method Deep self-consistent learning using neural networks to approximate both option prices and local volatility.
result Improved performance in terms of reduced interpolation and reprice errors compared to existing methods.
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…
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.
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. …
We extend Dupire's formula for stochastic interest rates and local volatility.
problem Deriving formulas for stochastic interest rates and local volatility.
method Generalizations of Dupire's formula for stochastic drift and local volatility.
result Validated the limits of the generalized Dupire formulae for specific cases.
In this paper we derive an easily computed approximation to European basket call prices for a local volatility jump-diffusion model. We apply the asymptotic expansion method to find the approximate value of the lower bound of European basket call prices. If the local volatility function is time independent then there i…
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 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.
This paper is devoted to the application of B-splines to volatility modeling, specifically the calibration of the leverage function in stochastic local volatility models and the parameterization of an arbitrage-free implied volatility surface calibrated to sparse option data. We use an extension of classical B-splines …
We introduce a multivariate diffusion model that is able to price derivative securities featuring multiple underlying assets. Each asset volatility smile is modeled according to a density-mixture dynamical model while the same property holds for the multivariate process of all assets, whose density is a mixture of mult…
Paper develops a new method for game options in local volatility models.
problem Optimal stopping in one-dimensional diffusion with general coefficients.
method Skorokhod embedding to construct recombining tree approximations.
result Construct nearly optimal stopping times with convergence rates.
Method calibrates local volatility and stochastic short rate models for equity-rate dynamics.
problem Joint calibration of local volatility and stochastic short rate models.
method Iterative approach using semimartingale optimal transport.
result Demonstrated performance on market data using European SPX options and cap interest rate options.
The local volatility model is a widely used for pricing and hedging financial derivatives. While its main appeal is its capability of reproducing any given surface of observed option prices---it provides a perfect fit---the essential component is a latent function which can be uniquely determined only in the limit of i…
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.
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…
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…
Study short maturity Asian options in jump-diffusion models with local volatility.
problem Analyzing Asian options pricing in models with jumps and local volatility.
method Asymptotic analysis for short maturity, considering fixed and floating strike options.
result Explicit results for Asian option prices in several models, including Merton, double-exponential, and Variance Gamma models.
We derive a forward equation for arbitrage-free barrier option prices, in terms of Markovian projections of the stochastic volatility process, in continuous semi-martingale models. This provides a Dupire-type formula for the coefficient derived by Brunick and Shreve for their mimicking diffusion and can be interpreted …
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.
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.
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…
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.
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…