A Novel Pricing Method for European Options Based on Fourier-Cosine Series Expansions
From MaRDI portal
Publication:99433
DOI10.1137/080718061zbMath1186.91214OpenAlexW2167698785MaRDI QIDQ99433
F. Fang, C. W. Oosterlee, Fang Fang, Cornelis W. Oosterlee
Publication date: January 2009
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/080718061
Applications of statistics to actuarial sciences and financial mathematics (62P05) Numerical methods (including Monte Carlo methods) (91G60) Characteristic functions; other transforms (60E10) Trigonometric approximation (42A10) Derivative securities (option pricing, hedging, etc.) (91G20) Numerical methods for trigonometric approximation and interpolation (65T40)
Related Items
Numerical valuation of Bermudan basket options via partial differential equations ⋮ Quantifying credit portfolio losses under multi-factor models ⋮ Isogeometric analysis in option pricing ⋮ Convergence of a Robust Deep FBSDE Method for Stochastic Control ⋮ Moments of integrated exponential Lévy processes and applications to Asian options pricing ⋮ Extension of stochastic volatility equity models with the Hull–White interest rate process ⋮ Efficiently pricing continuously monitored barrier options under stochastic volatility model with jumps ⋮ A finite volume – alternating direction implicit approach for the calibration of stochastic local volatility models ⋮ VALUATION OF VULNERABLE OPTIONS UNDER THE DOUBLE EXPONENTIAL JUMP MODEL WITH STOCHASTIC VOLATILITY ⋮ FAST COMPUTATION OF VANILLA PRICES IN TIME-CHANGED MODELS AND IMPLIED VOLATILITIES USING RATIONAL APPROXIMATIONS ⋮ SINH-ACCELERATION FOR B-SPLINE PROJECTION WITH OPTION PRICING APPLICATIONS ⋮ Smile and default: the role of stochastic volatility and interest rates in counterparty credit risk ⋮ Jumps and stochastic volatility in crude oil prices and advances in average option pricing ⋮ A Highly Efficient Shannon Wavelet Inverse Fourier Technique for Pricing European Options ⋮ COS method for option pricing under a regime-switching model with time-changed Lévy processes ⋮ Pricing and hedging guaranteed minimum withdrawal benefits under a general Lévy framework using the COS method ⋮ Singular Fourier–Padé series expansion of European option prices ⋮ On an efficient multiple time step Monte Carlo simulation of the SABR model ⋮ Fourier Cosine Expansions and Put–Call Relations for Bermudan Options ⋮ The COS Method for Pricing Options Under Uncertain Volatility ⋮ The SINC way: a fast and accurate approach to Fourier pricing ⋮ APPROXIMATING THE DENSITY OF THE TIME TO RUIN VIA FOURIER-COSINE SERIES EXPANSION ⋮ On the Fourier cosine series expansion method for stochastic control problems ⋮ An iterative splitting method for pricing European options under the Heston model ⋮ THE HESTON STOCHASTIC-LOCAL VOLATILITY MODEL: EFFICIENT MONTE CARLO SIMULATION ⋮ Monotonicity theorem for the uncertain fractional differential equation and application to uncertain financial market ⋮ Efficient Option Pricing by Frame Duality with the Fast Fourier Transform ⋮ A Fourier transform method for solving backward stochastic differential equations ⋮ QUANTO PRICING IN STOCHASTIC CORRELATION MODELS ⋮ Consistent Modelling of VIX and Equity Derivatives Using a 3/2 plus Jumps Model ⋮ The characteristic function of Gaussian stochastic volatility models: an analytic expression ⋮ Pricing ratchet equity index annuity with mortality risk by complex Fourier series method ⋮ Option pricing under stochastic volatility models with latent volatility ⋮ Intra‐Horizon expected shortfall and risk structure in models with jumps ⋮ Pricing equity-linked guaranteed minimum death benefits with surrender risk by complex Fourier series expansion method ⋮ An Efficient Transform Method for Asian Option Pricing ⋮ Two‐dimensional Haar wavelet based approximation technique to study the sensitivities of the price of an option ⋮ On a time-changed Lévy risk model with capital injections and periodic observation ⋮ Valuing variable annuities with path-dependent surrender guarantees under regime-switching Lévy models ⋮ A discrete-time hedging framework with multiple factors and fat tails: on what matters ⋮ Pricing European Options Under Stochastic Volatilities Models ⋮ Magic Points in Finance: Empirical Integration for Parametric Option Pricing ⋮ Fractional factorial designs for Fourier-cosine models ⋮ Lifting the Heston model ⋮ PRICING EUROPEAN OPTIONS ON REGIME-SWITCHING ASSETS: A COMPARATIVE STUDY OF MONTE CARLO AND FINITE-DIFFERENCE APPROACHES ⋮ A dimension and variance reduction Monte-Carlo method for option pricing under jump-diffusion models ⋮ On the modelling of nested risk-neutral stochastic processes with applications in insurance ⋮ Robust barrier option pricing by frame projection under exponential Lévy dynamics ⋮ Pricing Surrender Risk in Ratchet Equity-Index Annuities under Regime-Switching Lévy Processes ⋮ Modelling and Calibration of Stochastic Correlation in Finance ⋮ A Highly Efficient Numerical Method for the SABR Model ⋮ Pricing European-type, early-exercise and discrete barrier options using an algorithm for the convolution of Legendre series ⋮ An SFP–FCC method for pricing and hedging early-exercise options under Lévy processes ⋮ PERFORMANCE OF ROBUST HEDGES FOR DIGITAL DOUBLE BARRIER OPTIONS ⋮ Efficient Computation of Various Valuation Adjustments Under Local Lévy Models ⋮ COLLOCATING VOLATILITY: A COMPETITIVE ALTERNATIVE TO STOCHASTIC LOCAL VOLATILITY MODELS ⋮ SOME PRICING TOOLS FOR THE VARIANCE GAMMA MODEL ⋮ NEARLY EXACT OPTION PRICE SIMULATION USING CHARACTERISTIC FUNCTIONS ⋮ AN IMPLIED VOLATILITY MODEL DETERMINED BY CREDIT DEFAULT SWAPS ⋮ EFFICIENT PRICING AND RELIABLE CALIBRATION IN THE HESTON MODEL ⋮ Pricing Options Under Stochastic Volatility with Fourier-Cosine Series Expansions ⋮ Comparison and survey of finite difference methods for pricing American options under finite activity jump-diffusion models ⋮ Pricing high-dimensional Bermudan options using the stochastic grid method ⋮ The COS method for option valuation under the SABR dynamics ⋮ Fast exponential time integration scheme for option pricing with jumps ⋮ LOCAL STOCHASTIC VOLATILITY WITH JUMPS: ANALYTICAL APPROXIMATIONS ⋮ Option Pricing in Some Non-Lévy Jump Models ⋮ Computing the Gerber–Shiu function by frame duality projection ⋮ Pitfalls of the Fourier Transform Method in Affine Models, and Remedies ⋮ The Dynamic Correlation Model and Its Application to the Heston Model ⋮ OU models based on positive and negative subordinate processes applying in SHIBOR time series analysis and derivative pricing – through discrete differential method ⋮ BENCHOP – The BENCHmarking project in option pricing ⋮ Pricing Bermudan options under Merton jump-diffusion asset dynamics ⋮ Efficient pricing and hedging under the double Heston stochastic volatility jump-diffusion model ⋮ SWING OPTION PRICING BY DYNAMIC PROGRAMMING WITH B-SPLINE DENSITY PROJECTION ⋮ Polynomial Processes for Power Prices ⋮ Stochastic volatility double-jump-diffusions model: the importance of distribution type of jump amplitude ⋮ American option pricing under the double Heston model based on asymptotic expansion ⋮ The stochastic collocation Monte Carlo sampler: highly efficient sampling from ‘expensive’ distributions ⋮ Generative Bayesian neural network model for risk-neutral pricing of American index options ⋮ Calibration and advanced simulation schemes for the Wishart stochastic volatility model ⋮ Implied Lévy volatility ⋮ CREDIT MODELING UNDER JUMP DIFFUSIONS WITH EXPONENTIALLY DISTRIBUTED JUMPS — STABLE CALIBRATION, DYNAMICS AND GAP RISK ⋮ Fourier-Cosine Method for Finite-Time Gerber--Shiu Functions ⋮ Lookback option pricing using the Fourier transform B-spline method ⋮ ALGORITHMIC COUNTERPARTY CREDIT EXPOSURE FOR MULTI-ASSET BERMUDAN OPTIONS ⋮ Pricing discrete barrier options and credit default swaps under Lévy processes ⋮ Valuation of forward start options under affine jump-diffusion models ⋮ An efficient pricing method for rainbow options based on two-dimensional modified sine–sine series expansions ⋮ A Fourier Cosine Method for an Efficient Computation of Solutions to BSDEs ⋮ Application of power series approximation techniques to valuation of European style options ⋮ A functional analysis approach to the static replication of European options ⋮ Informative option portfolios in filter design for option pricing models ⋮ The affine Heston model with correlated Gaussian interest rates for pricing hybrid derivatives ⋮ Laplace transform approach to option pricing for time-changed Brownian models ⋮ Speed and biases of Fourier-based pricing choices: a numerical analysis ⋮ A stochastic local volatility technique for TARN options ⋮ Asymptotic expansion method for pricing and hedging American options with two-factor stochastic volatilities and stochastic interest rate ⋮ Numerical aspects of integration in semi-closed option pricing formulas for stochastic volatility jump diffusion models ⋮ Numerical valuation of European and American options under Merton's model ⋮ Finite-time expected present value of operating costs until ruin in a Cox risk model with periodic observation ⋮ Evaluation of integrals with fractional Brownian motion for different Hurst indices ⋮ Valuation of guaranteed minimum maturity benefits under mean reversion and jump models with surrender risk ⋮ Valuation of variable annuities with guaranteed minimum maturity benefits and periodic fees ⋮ Valuing equity-linked guaranteed minimum death benefits with \textit{European}-style \textit{Asian} payoffs under a regime switching jump-diffusion model ⋮ Closed-form option pricing for exponential Lévy models: a residue approach ⋮ Deep xVA Solver: A Neural Network–Based Counterparty Credit Risk Management Framework ⋮ Nonparametric estimation of some dividend problems in the perturbed compound Poisson model ⋮ Fast barrier option pricing by the COS BEM method in Heston model (with Matlab code) ⋮ Hedging at-the-money digital options near maturity ⋮ Valuation and optimal surrender of variable annuities with guaranteed minimum benefits and periodic fees ⋮ Pricing discretely monitored Asian options under regime-switching and stochastic volatility models with jumps ⋮ Can a Machine Correct Option Pricing Models? ⋮ Rough Heston Models with Variable Vol-of-Vol and Option Pricing ⋮ Forward starting options pricing with double stochastic volatility, stochastic interest rates and double jumps ⋮ Importance sampling and statistical Romberg method for Lévy processes ⋮ Efficient VaR and expected shortfall computations for nonlinear portfolios within the delta-gamma approach ⋮ Multigrid method for pricing European options under the CGMY process ⋮ Calibration and simulation of Heston model ⋮ Tempered stable structural model in pricing credit spread and credit default swap ⋮ An analytical approximation for single barrier options under stochastic volatility models ⋮ Computation of Greeks using binomial trees in a jump-diffusion model ⋮ Recombined multinomial tree based on saddle-point approximation and its application to Lévy models options pricing ⋮ Option pricing with Legendre polynomials ⋮ A Shannon wavelet method for pricing foreign exchange options under the Heston multi-factor CIR model ⋮ Estimating the time value of ruin in a Lévy risk model under low-frequency observation ⋮ Binomial tree method for option pricing: discrete cosine transform approach ⋮ A dimension reduction Shannon-wavelet based method for option pricing ⋮ A comparative study on time-efficient methods to price compound options in the Heston model ⋮ Pricing early-exercise and discrete barrier options by Fourier-cosine series expansions ⋮ The Jacobi stochastic volatility model ⋮ Valuation of guaranteed minimum maturity benefits under generalised regime-switching models using the Fourier cosine method ⋮ Consistent pricing of VIX and equity derivatives with the \(4/2\) stochastic volatility plus jumps model ⋮ A unified approach to Bermudan and barrier options under stochastic volatility models with jumps ⋮ Two-dimensional Shannon wavelet inverse Fourier technique for pricing European options ⋮ Equity-linked annuity pricing with cliquet-style guarantees in regime-switching and stochastic volatility models with jumps ⋮ The evaluation of barrier option prices under stochastic volatility ⋮ Asian options pricing in Hawkes-type jump-diffusion models ⋮ Pricing early-exercise and discrete barrier options by Shannon wavelet expansions ⋮ Pricing Bermudan options under local Lévy models with default ⋮ A Shannon wavelet method for pricing American options under two-factor stochastic volatilities and stochastic interest rate ⋮ Early exercise boundaries for American-style knock-out options ⋮ The evaluation of American options in a stochastic volatility model with jumps: an efficient finite element approach ⋮ An efficient algorithm for Bermudan barrier option pricing ⋮ An efficient algorithm based on eigenfunction expansions for some optimal timing problems in finance ⋮ On the data-driven COS method ⋮ Analytical pricing of American options ⋮ Double discretization difference schemes for partial integrodifferential option pricing jump diffusion models ⋮ Efficient numerical Fourier methods for coupled forward-backward SDEs ⋮ A regression-based numerical scheme for backward stochastic differential equations ⋮ Analytical approximation for distorted expectations ⋮ The Kolmogorov forward fractional partial differential equation for the CGMY-process with applications in option pricing ⋮ A regime switching fractional Black-Scholes model and European option pricing ⋮ A high-order finite difference method for option valuation ⋮ Pricing of early-exercise Asian options under Lévy processes based on Fourier cosine expansions ⋮ A Fourier-cosine method for pricing discretely monitored barrier options under stochastic volatility and double exponential jump ⋮ Statistical estimation for some dividend problems under the compound Poisson risk model ⋮ Pricing inflation products with stochastic volatility and stochastic interest rates ⋮ Pricing EIA with cliquet-style guarantees under time-changed Lévy models by frame duality projection ⋮ Efficient pricing of commodity options with early-exercise under the Ornstein-Uhlenbeck process ⋮ Estimating the discounted density of the deficit at ruin by Fourier cosine series expansion ⋮ Operator splitting schemes for the two-asset Merton jump-diffusion model ⋮ The use of power numeraires in option pricing ⋮ On the calibration of the 3/2 model ⋮ A Gamma Ornstein-Uhlenbeck model driven by a Hawkes process ⋮ On a one time-step Monte Carlo simulation approach of the SABR model: application to European options ⋮ Equity-linked guaranteed minimum death benefits with dollar cost averaging ⋮ Pricing basket options by polynomial approximations ⋮ Finite-time dividend problems in a Lévy risk model under periodic observation ⋮ Pricing equity-linked death benefits by complex Fourier series expansion in a regime-switching jump diffusion model ⋮ RBF-PU method for pricing options under the jump-diffusion model with local volatility ⋮ Valuation of electricity storage contracts using the COS method ⋮ Integrated structural approach to credit value adjustment ⋮ Volatility swaps and volatility options on discretely sampled realized variance ⋮ Highly efficient Shannon wavelet-based pricing of power options under the double exponential jump framework with stochastic jump intensity and volatility ⋮ A general framework for discretely sampled realized variance derivatives in stochastic volatility models with jumps ⋮ IMEX schemes for pricing options under jump-diffusion models ⋮ A new calibration of the Heston stochastic local volatility model and its parallel implementation on GPUs ⋮ Unconditional positive stable numerical solution of partial integrodifferential option pricing problems ⋮ Peaks and jumps reconstruction with \(B\)-splines scaling functions ⋮ Pricing vulnerable claims in a Lévy-driven model ⋮ Radial basis function partition of unity methods for pricing vanilla basket options ⋮ Positive solutions of European option pricing with CGMY process models using double discretization difference schemes ⋮ RMOPI ⋮ Dual control Monte-Carlo method for tight bounds of value function under Heston stochastic volatility model ⋮ A neural network-based framework for financial model calibration ⋮ Fluctuation identities with continuous monitoring and their application to the pricing of barrier options ⋮ On contingent-claim valuation in continuous-time for volatility models of Ornstein-Uhlenbeck type ⋮ Model risk and discretisation of locally risk-minimising strategies ⋮ Efficient pricing of discrete arithmetic Asian options under mean reversion and jumps based on Fourier-cosine expansions ⋮ A Fourier-cosine method for finite-time ruin probabilities ⋮ Quantization meets Fourier: a new technology for pricing options ⋮ Hilbert transform, spectral filters and option pricing ⋮ Fourier-cosine method for ruin probabilities ⋮ A realized volatility approach to option pricing with continuous and jump variance components ⋮ A radial basis function approach to compute the first-passage probability density function in two-dimensional jump-diffusion models for financial and other applications ⋮ Estimating the Gerber-Shiu function in a compound Poisson risk model with stochastic premium income ⋮ The value of power-related options under spectrally negative Lévy processes ⋮ A positivity-preserving numerical scheme for option pricing model with transaction costs under jump-diffusion process ⋮ Efficient pricing of European options on two underlying assets by frame duality ⋮ Uncertainty quantification and Heston model ⋮ The \(\beta\)-Meixner model ⋮ Pricing some life-contingent lookback options under regime-switching Lévy models ⋮ Smiles \& smirks: volatility and leverage by jumps ⋮ Precise option pricing by the COS method -- how to choose the truncation range ⋮ Valuation of a DB underpin hybrid pension under a regime-switching Lévy model ⋮ Valuing equity-linked death benefits with a threshold expense structure under a regime-switching Lévy model ⋮ Efficient valuation of guaranteed minimum maturity benefits in regime switching jump diffusion models with surrender risk ⋮ Fourier-cosine method for Gerber-Shiu functions ⋮ What is beneath the surface? Option pricing with multifrequency latent states ⋮ Smile from the past: a general option pricing framework with multiple volatility and leverage components ⋮ Pricing and hedging European-style options in Lévy-based stochastic volatility models considering the leverage effect ⋮ Numerical Fourier method and second-order Taylor scheme for backward SDEs in finance