This paper deals with a high-order accurate implicit finite-difference approach to the pricing of barrier options. In this way various types of barrier options are priced, including barrier options paying rebates, and options on dividend-paying-stocks. Moreover, the barriers may be monitored either continuously or disc…
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48 results for “discrete barrier options”
New Monte Carlo method for calculating sensitivities of barrier options.
problem Calculating sensitivities for discontinuous payoff functions in barrier options.
method Combining one-step survival idea with stable differentiation approach.
result Calculated sensitivities for different types of barrier options.
A fast numerical method for pricing double barrier options using Lagrange interpolation.
problem Pricing discrete double barrier knock-out call options efficiently.
method Approximating recursive solutions of the heat equation with Lagrange interpolation on Jacobi polynomials nodes.
result The method significantly reduces CPU time as the number of monitoring dates increases.
The presence of discrete dividends complicates the derivation and form of pricing formulas even for vanilla options. Existing analytic, numerical, and theoretical approximations provide results of varying quality and performance. Here, we compare the analytic approach, developed and effective for European puts and call…
We examine optimal quadratic hedging of barrier options in a discretely sampled exponential Lévy model that has been realistically calibrated to reflect the leptokurtic nature of equity returns. Our main finding is that the impact of hedging errors on prices is several times higher than the impact of other pricing bias…
The CONLeg method prices and hedges various option types using Legendre series.
problem Pricing and hedging European-type, early-exercise, and discrete-monitored barrier options.
method Algorithm for the convolution of Legendre series (CONLeg method) applied to Levy process.
result High accuracy in pricing and hedging, especially for deep out-of-the-money and long/mature options.
Fluctuation identities with continuous monitoring and their application to price barrier optionsq-fin.CP
New numerical method for pricing barrier options with continuous monitoring.
problem Pricing barrier options with continuous monitoring of underlying asset.
method Developed a numerical scheme to calculate fluctuation identities for exponential Lévy processes.
result Error analysis shows continuous monitoring limits discretely monitored scheme's accuracy.
In this Article, a fast numerical numerical algorithm for pricing discrete double barrier option is presented. According to Black-Scholes model, the price of option in each monitoring date can be evaluated by a recursive formula upon the heat equation solution. These recursive solutions are approximated by using Legend…
Fast Calculation of Credit Exposures for Barrier and Bermudan options using Chebyshev interpolationq-fin.CP
New method calculates credit exposures for complex options efficiently.
problem Efficient calculation of credit exposures for complex options.
method Dynamic Chebyshev method for closed-form approximation.
result Highly efficient evaluation of credit exposures for large paths.
Sequential Monte Carlo (SMC) methods have successfully been used in many applications in engineering, statistics and physics. However, these are seldom used in financial option pricing literature and practice. This paper presents SMC method for pricing barrier options with continuous and discrete monitoring of the barr…
An efficient conditioning technique, the so-called Brownian Bridge simulation, has previously been applied to eliminate pricing bias that arises in applications of the standard discrete-time Monte Carlo method to evaluate options written on the continuous-time extrema of an underlying asset. It is based on the simple a…
A simple and efficient numerical method for pricing discretely monitored early-exercise optionsq-fin.CP
A fast method for pricing various financial options.
problem Efficient pricing of discretely monitored early-exercise options.
method A quadrature technique-based method using elementary calculations and a fixed grid.
result Convergence rate of and complexity of .
Spectral filters enhance option pricing methods using Hilbert transforms.
problem Improving convergence rates of option pricing methods.
method Using spectral filters to improve convergence of numerical schemes based on discrete Hilbert transforms.
result Improved convergence rates, especially polynomial convergence, achieved with spectral filtering.
Efficient evaluation of double-barrier options and joint cpdf of a Lévy process and its two extremaq-fin.CP
Fast method developed for pricing barrier options and joint Lévy process distributions.
problem Accurate pricing of barrier options and joint distributions in Lévy models.
method Dual space calculations, Wiener-Hopf factorization, sinh-deformations, Gaver-Wynn Rho acceleration.
result Achieves precision of in seconds and in fractions of a second.
The paper calculates prices for multi-step barrier options under the Black-Scholes model.
problem Calculating prices for multi-step barrier options with varying barriers and time steps.
method Derives a general, explicit expression for option prices using the Black-Scholes model and a multi-step reflection principle.
result Derives a multi-step reflection principle that generalizes the reflection principle of Brownian motion.
Hamiltonian method applied to floating barrier options pricing.
problem Pricing of floating barrier options.
method Hamiltonian approach in quantum mechanics applied to barrier options.
result Analytical expressions for pricing kernel and option price derived.
Path Integral Method for Proportional Step and Proportional Double-Barrier Step Option Pricingq-fin.PR
Path integral method calculates barrier option prices.
problem Barrier option pricing in finance.
method Path integral method applied to trapezoid and square potential barriers.
result Analytical expressions for option pricing derived.
New method improves barrier option pricing for high volatility assets.
problem Efficient pricing of barrier options on high volatility assets.
method Subset Simulation for barrier option pricing.
result The method outperforms standard Monte Carlo and multilevel Monte Carlo approaches.
Deep learning solves barrier options with stochastic volatility.
problem Solving barrier options with stochastic volatility.
method Unsupervised deep learning neural networks trained to satisfy PDE and boundary conditions.
result Neural networks accurately price barrier options in a single framework.
Semi-analytic pricing of double barrier options with time-dependent barriers and rebates at hitq-fin.CP
Efficient semi-analytic methods for pricing double barrier options with time-dependent parameters.
problem Pricing and calibration of double barrier options with time-dependent parameters.
method Two approaches: General Integral transform method and Heat Potential method.
result Semi-analytic techniques are more efficient for pricing double barrier options than traditional numerical methods.
Unified pricing method for FX options with barriers.
problem Calculating the value and sensitivities of FX options with barriers.
method Unified Vanna-Volga pricing technique for single and double barrier FX options.
result Derivation of closed formulas for Delta, Vega, Vanna, and Volga.
Efficient inverse -transform and pricing barrier and lookback options with discrete monitoringmath.NA
The paper derives formulas for option pricing and random walk expectations.
problem Calculating the price of barrier and lookback options.
method Inverse Z-transform, Fourier/Laplace inversion, Wiener-Hopf factorization, and numerical methods.
result Efficient numerical methods for option pricing are developed.
In this article, we study the problem of pricing defaultable bond with discrete default intensity and barrier under constant risk free short rate using higher order binary options and their integrals. In our credit risk model, the risk free short rate is a constant and the default event occurs in an expected manner whe…
Barrier Option Pricingmath.AP
We use Lie symmetry methods to price certain types of barrier options. Usually Lie symmetry methods cannot be used to solve the Black-Scholes equation for options because the function defining the maturity condition for an option is not smooth. However, for barrier options, this restriction can be accommodated and a sy…
Study efficient pricing for barrier options in stochastic-volatility models with leverage correction.
problem Barrier options are sensitive to volatility dynamics, especially leverage, making accurate pricing difficult.
method Developed a class of continuous-path stochastic-clock volatility models and a systematic small-ρ expansion to incorporate leverage.
result Transform-only pricing formulas for barrier derivatives are fast and numerically stable, even for negative leverage.
We provided an analytical representation of the price of a barrier option with one type of special moving barrier. We consider the case that risk free rate, dividend rate and stock volatility are time dependent. We get a pricing formula and put call parity for barrier option when the moving barrier has a special relati…
We determine the price of digital double barrier options with an arbitrary number of barrier periods in the Black-Scholes model. This means that the barriers are active during some time intervals, but are switched off in between. As an application, we calculate the value of a structure floor for structured notes whose …
Paper applies subdiffusive dynamics to American and barrier options pricing.
problem Valuation of American and barrier options in subdiffusive financial models.
method Proposes weighted finite difference and Longstaff-Schwartz methods for valuation.
result Numerical valuation of American and barrier options demonstrated.
Path integral method calculates PDBS option prices with time-dependent parameters.
problem Pricing proportional double-barrier step options with time-dependent interest rates and volatilities.
method Path integral method applied to a quantum mechanical analogy of barrier options.
result Derivation of pricing kernel for PDBS options with time-dependent parameters.
A time-dependent double-barrier option is a derivative security that delivers the terminal value at expiry if neither of the continuous time-dependent barriers $b_\pm:[0,T]\to \RR_+$ have been hit during the time interval . Using a probabilistic approach we obtain a decomposition of the barrier opti…
In this paper we analyse financial implications of exchangeability and similar properties of finite dimensional random vectors. We show how these properties are reflected in prices of some basket options in view of the well-known put-call symmetry property and the duality principle in option pricing. A particular atten…
Finite element method for SABR model pricing under various interest rates.
problem Pricing vanilla and barrier options under the SABR stochastic volatility model.
method Finite element discretization of non-symmetric Dirichlet forms for degenerate parabolic equations.
result Well-posedness of the variational formulation and error analysis for finite element discretization.
New efficient method for inverse Z-transform reduces complexity significantly.
problem Efficient numerical realization of inverse Z-transform for large n.
method Derives sufficient conditions for new scheme, applies to option pricing.
result Significant reduction in complexity for large n, especially for European options.
We demonstrate effectiveness of the first-order algorithm from [Milstein, Tretyakov. Theory Prob. Appl. 47 (2002), 53-68] in application to barrier option pricing. The algorithm uses the weak Euler approximation far from barriers and a special construction motivated by linear interpolation of the price near barriers. I…
New formulas for barrier options in stochastic volatility models with nonzero correlation.
problem Calculating barrier options prices in models with nonzero correlation.
method Derivation of two novel closed-form formulas: Hull and White type and Alòs-like decomposition.
result Closed-form formulas for barrier options in stochastic volatility models with nonzero correlation.
Analytical model prices options with moving barriers under non-Gaussian distributions.
problem Pricing options with moving barriers under non-Gaussian distributions.
method Path-integral formalism adapted from galaxy formation models, incorporating higher-order cumulants.
result Analytical pricing model for vanilla and barrier options without volatility smile.
A new method uses deep learning to price barrier options.
problem Pricing barrier options with boundary conditions.
method Forward deep BSDEs with added nodes for barrier conditions.
result Can handle any barrier condition and boundary conditions.
This note re-addresses the Paris barrier options proposed by Yor and collaborators and their valuation using the Laplace transform approach. The notion of Paris barrier options, based on excursion theory and using the Brownian meander, is extended such that their valuation is now possible at any point during their life…
Paper approximates first passage time for tempered stable process for option pricing.
problem Pricing perpetual American options and barrier options using first passage time.
method Approximates characteristic function using martingale approach.
result Provides explicit or indirect numerical method for characteristic function of first passage time.
We show that prices and shortfall risks of game (Israeli) barrier options in a sequence of binomial approximations of the Black--Scholes (BS) market converge to the corresponding quantities for similar game barrier options in the BS market with path dependent payoffs and the speed of convergence is estimated, as well. …
We propose an efficient lattice procedure which permits to obtain European and American option prices under the Black and Scholes model for digital options with barrier features. Numerical results show the accuracy of the proposed method.
Study short-term behavior of up-and-in barrier options using Malliavin calculus.
problem Analyzing the decay rate of up-and-in barrier option prices as maturity decreases.
method Use Malliavin calculus to analyze the law of the supremum of the log-price process.
result Derive upper bound on asymptotic decay rate of up-and-in barrier option prices.
The paper uses a Hamiltonian method to price barrier options under Vasicek interest rate model.
problem Option pricing under Vasicek interest rate model with time-varying interest rates.
method Splitting time to maturity into infinite steps and using quantum mechanics methods for matrix elements, derived pricing kernel and integral expression.
result Numerical results of option prices as functions of underlying asset price, floating rate, and regression rate.
This paper presents a new asymptotic expansion method for pricing continuously monitoring barrier options. In particular, we develops a semi-group expansion scheme for the Cauchy-Dirichlet problem in the second-order parabolic partial differential equations (PDEs) arising in barrier option pricing. As an application, w…
Deep learning solves PDEs with boundary conditions for barrier options.
problem Solving PDEs with boundary conditions for barrier options.
method Employing deep learning to approximate solutions of the PDE with boundary conditions.
result Deep learning can solve PDEs with boundary conditions for barrier options.
Toward an efficient hybrid method for pricing barrier options on assets with stochastic volatilityq-fin.CP
Efficient hybrid method for pricing barrier options with stochastic volatility.
problem Valuation of barrier options on assets with stochastic volatility.
method Combining Monte Carlo simulation and semi-analytical heat potential method.
result Our method provides better accuracy and is orders of magnitude faster than existing methods.
Develops semi-closed form solutions for barrier and American options on time-dependent OU process.
problem Valuation of barrier and American options on a time-dependent Ornstein-Uhlenbeck process.
method Semi-closed form solutions involving numerical solution of Fredholm equations and integration of Jacobi theta functions.
result Method is more efficient than backward finite difference method and can be as efficient as forward finite difference solver with better accuracy and stability.
Improved barrier option pricing in Heston model using COS-BEM method.
problem Efficient barrier option pricing in the Heston model.
method Combining Fourier-cosine series (COS) method with Boundary Element Method (BEM).
result Significant computational efficiency improvement and BEM attractiveness for practitioners.