Asymptotic behavior of the stock price distribution density and implied volatility in stochastic volatility models

DOI10.1007/s00245-009-9085-xzbMath1208.91172arXiv0906.0392OpenAlexW1966935143MaRDI QIDQ1959682

Elias M. Stein, Archil Gulisashvili

Publication date: 7 October 2010

Published in: Applied Mathematics and Optimization (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0906.0392

zbMATH Keywords

stock priceasymptotic formulasBessel processesOrnstein-Uhlenbeck processesimplied volatilityHeston modelCIR processesmixing distribution densityStein-Stein model

Mathematics Subject Classification ID

Statistical methods; risk measures (91G70) Financial applications of other theories (91G80)

Related Items

On the Valuation of Discrete Asian Options in High Volatility Environments ⋮ ASYMPTOTIC EQUIVALENCE IN LEE'S MOMENT FORMULAS FOR THE IMPLIED VOLATILITY, ASSET PRICE MODELS WITHOUT MOMENT EXPLOSIONS, AND PITERBARG'S CONJECTURE ⋮ ASYMPTOTICS OF THE TIME-DISCRETIZED LOG-NORMAL SABR MODEL: THE IMPLIED VOLATILITY SURFACE ⋮ On refined volatility smile expansion in the Heston model ⋮ On the density of log-spot in the Heston volatility model ⋮ Two-Sided Estimates for Distribution Densities in Models with Jumps ⋮ Large Deviation Principle for Volterra Type Fractional Stochastic Volatility Models ⋮ Tail probability estimates for additive functionals ⋮ Implied Volatility of Basket Options at Extreme Strikes ⋮ On Singularities in the Heston Model ⋮ On the Probability Density Function of Baskets ⋮ Extreme-strike asymptotics for general Gaussian stochastic volatility models ⋮ Large deviation principles for stochastic volatility models with reflection ⋮ Shapes of Implied Volatility with Positive Mass at Zero ⋮ From Moment Explosion to the Asymptotic Behavior of the Cumulative Distribution for a Random Variable ⋮ ASYMPTOTIC BEHAVIOR OF DISTRIBUTION DENSITIES IN MODELS WITH STOCHASTIC VOLATILITY. I ⋮ Marginal Density Expansions for Diffusions and Stochastic Volatility I: Theoretical Foundations ⋮ Marginal Density Expansions for Diffusions and Stochastic Volatility II: Applications ⋮ On contingent-claim valuation in continuous-time for volatility models of Ornstein-Uhlenbeck type ⋮ Quantization meets Fourier: a new technology for pricing options ⋮ Large-maturity regimes of the Heston forward smile ⋮ Discrete-time approximation of functionals in models of Ornstein-Uhlenbeck type, with applications to finance ⋮ Generalized Arbitrage-Free SVI Volatility Surfaces ⋮ Small-time asymptotics for Gaussian self-similar stochastic volatility models ⋮ Asymptotic Analysis of Stock Price Densities and Implied Volatilities in Mixed Stochastic Models ⋮ Asymptotics of Forward Implied Volatility

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Asymptotic behavior of the distribution of the stock price in models with stochastic volatility: the Hull-White model
• A survey and some generalizations of Bessel processes
• Moment explosions in stochastic volatility models
• A Theory of the Term Structure of Interest Rates
• Ornstein–Uhlenbeck process with quadratic killing
• IMPLIED VOLATILITY IN THE HULL-WHITE MODEL
• ASYMPTOTIC BEHAVIOR OF DISTRIBUTION DENSITIES IN MODELS WITH STOCHASTIC VOLATILITY. I
• REGULAR VARIATION AND SMILE ASYMPTOTICS
• A decomposition of Bessel Bridges
• The log-normal approximation in financial and other computations
• THE MOMENT FORMULA FOR IMPLIED VOLATILITY AT EXTREME STRIKES
• Bessel Processes, the Integral of Geometric Brownian Motion, and Asian Options
• A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options
• Stock Price Distributions with Stochastic Volatility: An Analytic Approach