Analytical Expansions for Parabolic Equations

DOI10.1137/130949968zbMath1332.35140arXiv1312.3314OpenAlexW3123115509MaRDI QIDQ5264986

Stefano Pagliarani, Matthew Lorig, Andrea Pascucci

Publication date: 21 July 2015

Published in: SIAM Journal on Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.3314

zbMATH Keywords

Cauchy problempolynomial expansionclosed-form asymptotic approximationsgeneral parabolic partial differential equationshort-time error estimates

Mathematics Subject Classification ID

Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of equilibrium problems in solid mechanics (74G10) Derivative securities (option pricing, hedging, etc.) (91G20) Initial value problems for second-order parabolic equations (35K15)

Related Items (23)

CDS calibration under an extended JDCEV model ⋮ Intrinsic expansions for averaged diffusion processes ⋮ EXPLICIT IMPLIED VOLATILITIES FOR MULTIFACTOR LOCAL‐STOCHASTIC VOLATILITY MODELS ⋮ Analytical approximations of non-linear SDEs of McKean-Vlasov type ⋮ Optimal static quadratic hedging ⋮ Portfolio Optimization under Local-Stochastic Volatility: Coefficient Taylor Series Approximations and Implied Sharpe Ratio ⋮ Asymptotics for $$d$$ -Dimensional Lévy-Type Processes ⋮ A Fourier-based Picard-iteration approach for a class of McKean–Vlasov SDEs with Lévy jumps ⋮ Pricing Bermudan options under local Lévy models with default ⋮ Options on bonds: implied volatilities from affine short-rate dynamics ⋮ Approximate solutions to second-order parabolic equations: evolution systems and discretization ⋮ Small time chaos approximations for heat kernels of multidimensional diffusions ⋮ Intrinsic Taylor formula for Kolmogorov-type homogeneous groups ⋮ Small-Time Asymptotics under Local-Stochastic Volatility with a Jump-to-Default: Curvature and the Heat Kernel Expansion ⋮ Analytical approximation of the transition density in a local volatility model ⋮ The implied Sharpe ratio ⋮ Expansions asymptotiques pour équations paraboliques dégénérées ⋮ OPTIMAL LIQUIDATION UNDER STOCHASTIC PRICE IMPACT ⋮ INDIFFERENCE PRICES AND IMPLIED VOLATILITIES ⋮ A VOLATILITY-OF-VOLATILITY EXPANSION OF THE OPTION PRICES IN THE SABR STOCHASTIC VOLATILITY MODEL ⋮ Pricing approximations and error estimates for local Lévy-type models with default ⋮ Sovereign CDS Calibration Under a Hybrid Sovereign Risk Model ⋮ PDE models for the pricing of a defaultable coupon-bearing bond under an extended JDCEV model

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