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…
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48 results for “Stochastic Local Volatility”
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.
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.
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.
Short-maturity asymptotics for VIX and European options in local-stochastic volatility modelsq-fin.PR
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.
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.
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.
Non--regular McKean--Vlasov equations and calibration problem in local stochastic volatility modelsmath.PR
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.
Study shows conditions for local martingales in SDEs with stochastic volatility.
problem Conditions for local martingales in stochastic differential equations with stochastic volatility.
method Examine sufficient conditions for components of SDEs to be strict local martingales or martingales.
result Components of SDEs can be strict local martingales or martingales under certain conditions.
We solve the SLV model calibration problem using inverse-problem techniques.
problem Calibrating the SLV model given a local volatility surface and stochastic volatility parameters.
method Regularization techniques from inverse-problem theory.
result Stable and robust algorithm for SLV model calibration.
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.
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).
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.
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…
Localizing Volatilitiesmath.PR
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…
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.
Study reveals how implied and local volatility behave at extreme strikes.
problem Understanding volatility at extreme strike prices in stochastic models.
method New Tauberian theorem applied to moment generating functions.
result Sharp asymptotic expansions of local and implied volatility.
This study simplifies rough Heston model's conditional density equation.
problem Analyzing rough volatility in financial models.
method Pathwise transformation and Fokker-Planck formulation of conditional density equation.
result Transformed equation yields deterministic PDE with path-dependent coefficients.
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.
Existence of a calibrated regime switching local volatility model and new fake Brownian motionsmath.PR
New fake Brownian motions derived from calibrated LSV models.
problem Calibrating LSV models to market data with stochastic volatility.
method Particle methods and McKean SDEs for calibration; Fokker-Planck PDEs for existence proof.
result Existence of new fake Brownian motions derived from calibrated LSV models.
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.
Derives new equations for stochastic volatility models.
problem Modeling local-stochastic-volatility models and their derivatives.
method Conditional forward equation, Dupire stochastic PDE, rolling expiry vanilla option SPDE.
result New equations for LSV models and their derivatives.
Derives new equations for volatility models and option pricing.
problem Modeling and pricing options in local-stochastic-volatility models.
method Develops conditional forward equations and Dupire stochastic PDEs.
result Derives new SPDE for vanilla options.
We approximate prices of various financial claims using a combination of expansions.
problem Approximating prices of financial claims in a complex volatility setting.
method Combining Taylor series expansions of diffusion coefficients with an expansion in correlation parameter.
result Rigorous accuracy results for European-style claims, and numerical examples for barrier-style claims.
Efficient PDE method calibrates local volatility with stochastic interest rates.
problem Calibrating local volatility models with stochastic interest rates is time-consuming.
method Developed a PDE approach using ADI method to solve the forward equation.
result Effective and sufficient information for calibration and pricing is provided.
Study the averaging principle for non-autonomous slow-fast systems and apply it to financial local stochastic volatility models.
problem Understanding the behavior of non-autonomous slow-fast systems of stochastic differential equations.
method Prove the averaging principle under specific conditions and apply it to a financial model.
result Prices of derivatives converge to those calculated using the limit model under a risk-neutral measure.
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.
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…
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.
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.
Calibrates hybrid LSV models with stochastic rates using particle method and control variates.
problem Calibrating complex foreign exchange models with stochastic volatility and stochastic rates.
method Combines particle method with variance reduction techniques and control variates.
result Accelerates convergence in calibration process for a wide class of hybrid LSV models.
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.
New neural operator calibrates LSV models faster and more accurately.
problem Calibrating LSV models is slow, noisy, and sequential.
method Developed a projection-consistent neural operator.
result Calibration latency reduced from 98.5 to 0.6 ms.
New method solves SLV models faster using Lie algebra.
problem Local stochastic volatility models.
method Wei-Norman factorization method and Lie algebraic techniques.
result Reduces time-dependent SLV models to autonomous PDEs.
New method improves Euler approximation for local stochastic volatility models.
problem Well-posedness of Euler approximation for local stochastic volatility models.
method Start with a well-defined Euler approximation to the formal McKean-Vlasov equation, followed by a half-step scheme.
result Showed weak order one for the Euler discretization, plus error terms.
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.
Calibration of Local Volatility Models with Stochastic Interest Rates using Optimal Transportq-fin.MF
Method calibrates stock price models with stochastic interest rates using optimal transport.
problem Calibrating stock price models with stochastic interest rates.
method Non-parametric, semimartingale optimal transport, solving a fully non-linear Hamilton-Jacobi-Bellman equation.
result Fully calibrated model closest to a reference model in a defined cost function.
Stochastic Spot/Volatility Correlation in Stochastic Volatility Models and Barrier Option Pricingq-fin.PR
Most models for barrier pricing are designed to let a market maker tune the model-implied covariance between moves in the asset spot price and moves in the implied volatility skew. This is often implemented with a local volatility/stochastic volatility mixture model, where the mixture parameter tunes that covariance. T…
A general Multidimensional Monte Carlo Approach for Dynamic Hedging under stochastic volatilityq-fin.PR
In this work, we introduce a Monte Carlo method for the dynamic hedging of general European-type contingent claims in a multidimensional Brownian arbitrage-free market. Based on bounded variation martingale approximations for Galtchouk-Kunita-Watanabe decompositions, we propose a feasible and constructive methodology w…
Researchers prove a new measure for a financial volatility model.
problem Modeling financial volatility with a Hawkes process.
method Prove existence of equivalent martingale measures for a Heston-Hawkes model.
result Existence of a family of equivalent martingale measures for the model.
Inverting the Markovian projection, with an application to local stochastic volatility modelsmath.PR
We solve complex SDEs to model financial volatility.
problem Modeling financial volatility with rich dynamics.
method Proved existence and uniqueness of stationary solutions for specific SDEs.
result Calibrated local stochastic volatility models are possible.
New method for CMS derivatives pricing using Watanabe's expansions.
problem Pricing CMS derivatives under local and stochastic volatility.
method Malliavin's calculus and Watanabe's expansions applied to quadratic payoffs.
result Generic approximations for CMS derivatives pricing under various volatility models.
New SV models calibrated to market instruments using Schrodinger bridge approach.
problem Creating calibrated Stochastic Volatility Models to market instruments.
method Building a new class of SV models using Schrodinger bridge approach, with instantaneous volatility not modified.
result Models differ from local SV models and can be interpreted as martingale Schrodinger bridges.
New algorithm calibrates stochastic volatility models without errors.
problem Calibration errors in stochastic volatility models.
method Monte Carlo based LSV calibration algorithm for all models.
result Closed-form and exact calibration method with variance reduction.
Local equivalence found between Black-Scholes and Merton-Garman equations.
problem Restoring local symmetry in stock prices under stochastic volatility.
method Exploring gauge field theory to show local equivalence.
result Black-Scholes and Merton-Garman equations are locally equivalent.
On the Consistency of the Deterministic Local Volatility Function Model ('implied tree')cond-mat.stat-mech
We show that the frequent claim that the implied tree prices exotic options consistently with the market is untrue if the local volatilities are subject to change and the market is arbitrage-free. In the process, we analyse -- in the most general context -- the impact of stochastic variables on the P&L of a hedged port…
Investors optimize their portfolios to maximize utility under drawdown constraints and stochastic volatility.
problem Maximizing utility relative to maximum performance under drawdown constraints and stochastic volatility.
method Approximations through coefficient expansion and nonlinear transformations, numerically computed.
result Investors need a different portfolio strategy in stochastic volatility compared to constant volatility.
Calibration of Local-Stochastic and Path-Dependent Volatility Models to Vanilla and No-Touch Optionsq-fin.MF
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.