Asymptotic Expansion Approach in Finance

DOI10.1007/978-3-319-11605-1_13zbMath1418.91541OpenAlexW3040865015MaRDI QIDQ4560338

Akihiko Takahashi

Publication date: 11 December 2018

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://www.carf.e.u-tokyo.ac.jp/old/pdf/workingpaper/fseries/F356.pdf

zbMATH Keywords

greeksasymptotic expansionstochastic volatilityMalliavin calculusoption pricingderivativesinterest rateterm structure modelWatanabe theoryhedge

Mathematics Subject Classification ID

Asymptotic approximations, asymptotic expansions (steepest descent, etc.) (41A60) Applications of stochastic analysis (to PDEs, etc.) (60H30) Interest rates, asset pricing, etc. (stochastic models) (91G30) Derivative securities (option pricing, hedging, etc.) (91G20) Stochastic calculus of variations and the Malliavin calculus (60H07)

Related Items

A new efficient approximation scheme for solving high-dimensional semilinear PDEs: control variate method for deep BSDE solver, Asymptotic expansion for forward-backward SDEs with jumps, Derivatives pricing with market impact and limit order book, Acceleration of automatic differentiation of solutions to parabolic partial differential equations: a higher order discretization, An Arbitrary High Order Weak Approximation of SDE and Malliavin Monte Carlo: Analysis of Probability Distribution Functions, A second-order discretization with Malliavin weight and Quasi-Monte Carlo method for option pricing, High order weak approximation for irregular functionals of time-inhomogeneous SDEs, Time-inhomogeneous Gaussian stochastic volatility models: large deviations and super roughness, Second Order Discretization of Bismut--Elworthy--Li Formula: Application to Sensitivity Analysis

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Pricing exotic options and American options: a multidimensional asymptotic expansion approach
• Approximations for Asian options in local volatility models
• A semigroup expansion for pricing barrier options
• An approximation formula for basket option prices under local stochastic volatility with jumps: an application to commodity markets
• Coefficients of asymptotic expansions of SDE with jumps
• Basket options valuation for a local volatility jump-diffusion model with the asymptotic expansion method
• An asymptotic expansion scheme for optimal investment problems
• Large deviations and asymptotic methods in finance
• A new computational scheme for computing Greeks by the asymptotic expansion approach
• Asymptotic expansions for functionals of a Poisson random measure
• A remark on the asymptotic expansion of density function of Wiener functionals
• An asymptotic expansion approach to pricing financial contingent claims
• Financial modeling in a fast mean-reverting stochastic volatility environment
• A remark on a singular perturbation method for option pricing under a stochastic volatility model
• Analysis of Wiener functionals (Malliavin calculus) and its applications to heat kernels
• Precise asymptotics of certain Wiener functionals
• Asymptotic expansions of maximum likelihood estimators for small diffusions via the theory of Malliavin-Watanabe
• Forward-backward stochastic differential equations and their applications
• LIBOR and swap market models and measures
• On validity of the asymptotic expansion approach in contingent claim analysis
• An asymptotic expansion for forward-backward SDEs: a Malliavin calculus approach
• Representation theorems for backward stochastic differential equations
• Pricing discrete barrier options under stochastic volatility
• An FBSDE approach to American option pricing with an interacting particle method
• Perturbative expansion technique for non-linear FBSDEs with interacting particle method
• Stochastic calculus of variations in mathematical finance.
• Momentum-space approach to asymptotic expansion for stochastic filtering
• An asymptotic expansion approach to currency options with a market model of interest rates under stochastic volatility processes of spot exchange rates
• Pricing contingent claims with credit risk: asymptotic expansion approach
• Branching Markov processes. I
• Conditional expansions and their applications.
• The Asymptotic Expansion Approach to the Valuation of Interest Rate Contingent Claims
• NOTE ON AN EXTENSION OF AN ASYMPTOTIC EXPANSION SCHEME
• Composition with distributions of Wiener-Poisson variables and its asymptotic expansion
• Asymptotics Beats Monte Carlo: The Case of Correlated Local Vol Baskets
• An Affine Multicurrency Model with Stochastic Volatility and Stochastic Interest Rates
• Weak and strong Taylor methods for numerical solutions of stochastic differential equations
• Asymptotic Formulas with Error Estimates for Call Pricing Functions and the Implied Volatility at Extreme Strikes
• A HYBRID ASYMPTOTIC EXPANSION SCHEME: AN APPLICATION TO LONG-TERM CURRENCY OPTIONS
• An asymptotic expansion formula for up-and-out barrier option price under stochastic volatility model
• ANALYTICAL APPROXIMATION FOR NON-LINEAR FBSDEs WITH PERTURBATION SCHEME
• A generalized clark representation formula, with application to optimal portfolios
• FOURIER TRANSFORM METHOD WITH AN ASYMPTOTIC EXPANSION APPROACH: AN APPLICATION TO CURRENCY OPTIONS
• Analysis, Geometry, and Modeling in Finance
• PROBABILITY DISTRIBUTION AND OPTION PRICING FOR DRAWDOWN IN A STOCHASTIC VOLATILITY ENVIRONMENT
• Pricing Options on Scalar Diffusions: An Eigenfunction Expansion Approach
• SMALL-TIME ASYMPTOTICS FOR IMPLIED VOLATILITY UNDER THE HESTON MODEL
• On the moments of a multiple wiener-ito integral and the space induced by the polynomials of the integral
• Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation
• Application of brownian motion to the equation of kolmogorov-petrovskii-piskunov
• ALTERNATIVE CHARACTERIZATIONS OF AMERICAN PUT OPTIONS
• The Market Model of Interest Rate Dynamics
• Backward Stochastic Differential Equations in Finance
• A new approximate swaption formula in the LIBOR market model: an asymptotic expansion approach
• A GENERAL COMPUTATION SCHEME FOR A HIGH-ORDER ASYMPTOTIC EXPANSION METHOD
• THE MOMENT FORMULA FOR IMPLIED VOLATILITY AT EXTREME STRIKES
• An Asymptotic Expansion with Push-Down of Malliavin Weights
• The Small-Time Smile and Term Structure of Implied Volatility under the Heston Model
• ASYMPTOTICS OF IMPLIED VOLATILITY IN LOCAL VOLATILITY MODELS
• Closed-Form Expansion, Conditional Expectation, and Option Valuation
• Making mean-variance hedging implementable in a partially observable market
• On refined volatility smile expansion in the Heston model
• Spectral Expansions for Asian (Average Price) Options
• LOCAL STOCHASTIC VOLATILITY WITH JUMPS: ANALYTICAL APPROXIMATIONS
• LOWER BOUND APPROXIMATION TO BASKET OPTION VALUES FOR LOCAL VOLATILITY JUMP-DIFFUSION MODELS
• Fundamental equations of branching Markov processes
• Probabilistic Treatment of the Blowing up of Solutions for a Nonlinear Integral Equation
• On branching Markov processes
• Approximation of expectation of diffusion processes based on Lie algebra and Malliavin calculus
• Marginal Density Expansions for Diffusions and Stochastic Volatility I: Theoretical Foundations
• Marginal Density Expansions for Diffusions and Stochastic Volatility II: Applications
• Best approximation in inner product spaces
• Credit risk: Modelling, valuation and hedging
• A solution approach to valuation with unhedgeable risks