On validity of the asymptotic expansion approach in contingent claim analysis

DOI10.1214/aoap/1060202831zbMath1091.91037OpenAlexW1980610791MaRDI QIDQ1425481

Akihiko Takahashi, Naoto Kunitomo

Publication date: 21 March 2004

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://semanticscholar.org/paper/06f99311f3cb3276702ec93ddb31e91cb00fedd2

zbMATH Keywords

asymptotic expansionMalliavin calculusvaliditysmall disturbance asymptoticsValuation of financial contingent claimsWanatabe-Yoshida theory

Mathematics Subject Classification ID

Related Items (31)

Composition with distributions of Wiener-Poisson variables and its asymptotic expansion ⋮ An asymptotic expansion for forward-backward SDEs: a Malliavin calculus approach ⋮ A weak approximation with asymptotic expansion and multidimensional Malliavin weights ⋮ A new efficient approximation scheme for solving high-dimensional semilinear PDEs: control variate method for deep BSDE solver ⋮ On Error Estimates for Asymptotic Expansions with Malliavin Weights: Application to Stochastic Volatility Model ⋮ A new computational scheme for computing Greeks by the asymptotic expansion approach ⋮ Short-time at-the-money skew and rough fractional volatility ⋮ Asymptotic Expansion Approach in Finance ⋮ A Small Noise Asymptotic Expansion for Young SDE Driven by Fractional Brownian Motion: A Sharp Error Estimate With Malliavin Calculus ⋮ Control variate method for deep BSDE solver using weak approximation ⋮ A formula of small time expansion for Young SDE driven by fractional Brownian motion ⋮ A new algorithm for computing path integrals and weak approximation of SDEs inspired by large deviations and Malliavin calculus ⋮ APPROXIMATING LOCAL VOLATILITY FUNCTIONS OF STOCHASTIC VOLATILITY MODELS: A CLOSED-FORM EXPANSION APPROACH ⋮ Solving Kolmogorov PDEs without the curse of dimensionality via deep learning and asymptotic expansion with Malliavin calculus ⋮ A semigroup expansion for pricing barrier options ⋮ An asymptotic expansion approach to currency options with a market model of interest rates under stochastic volatility processes of spot exchange rates ⋮ Pricing discretely monitored barrier options: when Malliavin calculus expansions meet Hilbert transforms ⋮ Asymptotic expansion of a nonlinear oscillator with a jump-diffusion process ⋮ Solving backward stochastic differential equations with quadratic-growth drivers by connecting the short-term expansions ⋮ Pricing Ratchet Equity-Indexed Annuities with Early Surrender Risk in a CIR++ Model ⋮ An FBSDE approach to American option pricing with an interacting particle method ⋮ Perturbative expansion technique for non-linear FBSDEs with interacting particle method ⋮ Short-Term At-the-Money Asymptotics under Stochastic Volatility Models ⋮ Pricing Average and Spread Options Under Local-Stochastic Volatility Jump-Diffusion Models ⋮ Pricing derivatives using the asymptotic expansion approach: credit migration models with stochastic credit spreads ⋮ Closed-Form Expansions of Discretely Monitored Asian Options in Diffusion Models ⋮ Making mean-variance hedging implementable in a partially observable market ⋮ A polynomial scheme of asymptotic expansion for backward SDEs and option pricing ⋮ NOTE ON AN EXTENSION OF AN ASYMPTOTIC EXPANSION SCHEME ⋮ Pricing and exercising American options: an asymptotic expansion approach ⋮ Asymptotic expansion for a Black-Scholes model with small noise stochastic jump-diffusion interest rate

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Lectures on stochastic differential equations and Malliavin calculus
• An asymptotic expansion approach to pricing financial contingent claims
• Pricing options under stochastic interest rates: a new approach
• Analysis of Wiener functionals (Malliavin calculus) and its applications to heat kernels
• Asymptotic expansions of the distributions of the estimates of coefficients in a simultaneous equation system
• Asymptotic expansions of maximum likelihood estimators for small diffusions via the theory of Malliavin-Watanabe
• Malliavin calculus and asymptotic expansion for martingales
• The Asymptotic Expansion Approach to the Valuation of Interest Rate Contingent Claims
• Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation

This page was built for publication: On validity of the asymptotic expansion approach in contingent claim analysis