EXPANSION FORMULAS FOR EUROPEAN OPTIONS IN A LOCAL VOLATILITY MODEL

DOI10.1142/S0219024910005887zbMath1205.91153MaRDI QIDQ3580186

Eric Benhamou, Emmanuel Gobet, Mohammed Miri

Publication date: 11 August 2010

Published in: International Journal of Theoretical and Applied Finance (Search for Journal in Brave)

zbMATH Keywords

asymptotic expansionsTaylor expansionEuropean optionsCEV modellocal volatility modelsmall diffusion processDupire modelimplied Black-Scholes volatilitysecond and third order approximation

Mathematics Subject Classification ID

Stochastic ordinary differential equations (aspects of stochastic analysis) (60H10) Applications of stochastic analysis (to PDEs, etc.) (60H30) Derivative securities (option pricing, hedging, etc.) (91G20) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30)

Related Items (18)

Analytical formulas for a local volatility model with stochastic rates ⋮ On Error Estimates for Asymptotic Expansions with Malliavin Weights: Application to Stochastic Volatility Model ⋮ New Approximations in Local Volatility Models ⋮ Stability of Densities for Perturbed Diffusions and Markov Chains ⋮ ANALYTIC PRICING OF CoCo BONDS ⋮ Analytical approximation of the transition density in a local volatility model ⋮ Weak approximation of averaged diffusion processes ⋮ Expansions asymptotiques pour équations paraboliques dégénérées ⋮ EXPANSION FORMULAS FOR EUROPEAN QUANTO OPTIONS IN A LOCAL VOLATILITY FX-LIBOR MODEL ⋮ Pricing discretely monitored barrier options: when Malliavin calculus expansions meet Hilbert transforms ⋮ LOCAL STOCHASTIC VOLATILITY WITH JUMPS: ANALYTICAL APPROXIMATIONS ⋮ Smart expansion and fast calibration for jump diffusions ⋮ A decomposition formula for option prices in the Heston model and applications to option pricing approximation ⋮ EXPANSION FORMULAS FOR BIVARIATE PAYOFFS WITH APPLICATION TO BEST-OF OPTIONS ON EQUITY AND INFLATION ⋮ \(L_1\) and \(L_{\infty}\) stability of transition densities of perturbed diffusions ⋮ Closed-Form Expansions of Discretely Monitored Asian Options in Diffusion Models ⋮ Analytical Expansions for Parabolic Equations ⋮ The VIX Future in Bergomi Models: Fast Approximation Formulas and Joint Calibration with S&P 500 Skew

Cites Work

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• Pricing options under stochastic volatility: a power series approach
• Smart expansion and fast calibration for jump diffusions
• The Malliavin Calculus and Related Topics
• Equivalent Black volatilities
• Stochastic Volatility Model with Time‐dependent Skew

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