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.
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48 results for “Barrier condition”
We discuss the pricing methodology for Bonus Certificates and Barrier Reverse-Convertible Structured Products. Pricing for a European barrier condition is straightforward for products of both types and depends on an efficient interpolation of observed market option pricing. Pricing products We discuss the pricing metho…
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.
Root's barrier is continuous and finite under certain conditions.
problem Continuity of the root barrier function.
method Analyzing Skorokhod embedding problem and properties of target measures.
result The barrier function is continuous and finite under specified conditions.
We develop a conditional sampling scheme for pricing knock-out barrier options under the Linear Transformations (LT) algorithm from Imai and Tan (2006). We compare our new method to an existing conditional Monte Carlo scheme from Glasserman and Staum (2001), and show that a substantial variance reduction is achieved. W…
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…
The conditional-mean barrier helps diagnose deterministic surrogates missing uncertainty.
problem Uncertainty in deterministic surrogates for complex systems.
method Developed diagnostics to locate the conditional-mean barrier and prove its necessity for distributional objectives.
result Crossing the barrier requires a loss that scores distributions, not point predictions.
Research provides explicit NPV expressions for double barrier strategies.
problem Calculating expected NPVs of double barrier strategies for regular diffusions.
method Explicit expression using bivariate q-scale function with perturbation technique.
result Explicit expressions for expected NPVs are derived for certain cases.
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…
We propose a quasi-Monte Carlo algorithm for pricing knock-out and knock-in barrier options under the Heston (1993) stochastic volatility model. This is done by modifying the LT method from Imai and Tan (2006) for the Heston model such that the first uniform variable does not influence the stochastic volatility path an…
Barrier methods classify minimal submanifolds in hyperkaehler spaces.
problem Classifying compact minimal submanifolds in hyperkaehler spaces.
method Barrier argument and strong stability condition analysis.
result Results towards a classification of compact minimal submanifolds.
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…
IPMs struggle with hyperbolic spaces due to polynomially growing barrier parameters.
problem IPMs' efficiency is hindered in hyperbolic spaces.
method Analyzing the barrier parameter growth in hyperbolic and Hadamard spaces.
result The barrier parameter grows polynomially with the domain's diameter in hyperbolic spaces.
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.
Improved MLMC method for barrier options with non-Lipschitz coefficients.
problem Efficiency improvement for barrier option pricing with non-Lipschitz diffusion.
method Interpolated Drift Implicit Euler MLMC method, Lamperti transformation, Brownian bridge technique.
result Improved efficiency of MLMC for barrier options with non-Lipschitz coefficients.
In [8] Gerhardt proves longtime existence for the inverse mean curvature flow in globally hyperbolic Lorentzian manifolds with compact Cauchy hypersurface, which satisfy three main structural assumptions: a strong volume decay condition, a mean curvature barrier condition and the timelike convergence condition. Further…
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.
Study on existence and structure of P-area surfaces in Heisenberg group.
problem Existence and structure of P-area minimizing surfaces in the Heisenberg group.
method Characterization of existence and structure using an underlying vector field N, proving existence even without satisfying boundary conditions, and applying Barrier condition.
result Existence of P-area minimizing surfaces under certain conditions, providing new understanding of the Heisenberg group.
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.
Alternative solvability criterion for minimal surface equations and mean curvature flow.
problem Solvability of Dirichlet problem for minimal surface equation in non-mean convex domains.
method Introduces a structural condition from a second-order ODE to construct boundary barriers, applicable to unbounded domains and Hadamard manifolds.
result Allows solvability under geometric hypotheses different from classical Jenkins-Serrin theory, applicable to Euclidean space and mean curvature flow.
As is known, an option price is a solution to a certain partial differential equation (PDE) with terminal conditions (payoff functions). There is a close association between the solution of PDE and the solution of a backward stochastic differential equation (BSDE). We can either solve the PDE to obtain option prices or…
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…
This paper concerns the dual risk model, dual to the risk model for insurance applications, where premiums are surplus-dependent. In such a model premiums are regarded as costs, while claims refer to profits. We calculate the mean of the cumulative discounted dividends paid until ruin, if the barrier strategy is applie…
A scalable framework optimizes multi-asset portfolios with constraints.
problem Optimizing multi-asset portfolios with inequality constraints.
method Integrates neural policies with Pontryagin's Maximum Principle, enforcing feasibility via log-barrier regularization.
result Recover KKT-optimal policies in high-dimensional problems without violating constraints.
Ancient caloric functions on manifolds with polynomial growth are studied under volume doubling barrier.
problem Analyzing ancient caloric functions on manifolds beyond volume doubling.
method Time polynomial structure result on ancient caloric functions with polynomial growth.
result Finiteness result for ancient caloric functions is essentially sharp, except for multi-end cases.
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 …
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…
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.
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…
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.
Expectation propagation (EP) is a powerful approximate inference algorithm. However, a critical barrier in applying EP is that the moment matching in message updates can be intractable. Handcrafting approximations is usually tricky, and lacks generalizability. Importance sampling is very expensive. While Laplace propag…
We investigate the pricing of financial options under the 2-hypergeometric stochastic volatility model. This is an analytically tractable model that reproduces the volatility smile and skew effects observed in empirical market data. Using a regular perturbation method from asymptotic analysis of partial differential eq…
The study examines a semi-symmetric metric connection in perfect fluid space-time and phantom barriers.
problem Investigating the properties of semi-symmetric metric connections in perfect fluid space-time.
method Using concircularly semi-symmetric metric connections, the study derives conditions for quasi-Einstein manifolds and examines the scalar curvature of perfect fluid space-times.
result The study proves that in a perfect fluid space-time, the scalar curvature is constant and represents a phantom barrier.
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.
New method tackles bilevel optimization with polyhedral constraints.
problem Challenges in bilevel optimization with active-set changes and expensive Hessian inversions.
method Logarithmic barrier smoothing and proxy-gradient algorithm for differentiable approximation.
result Stationarity rates of in deterministic setting and under stochastic noise.
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.
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.
Post-training optimizes model performance beyond base model limits.
problem Optimizing sequence prediction models beyond the base model's support.
method Policy gradient (PG) and adaptive learning rate (LR) techniques.
result Post-training with PG can achieve near-optimal performance beyond the base model's support.
New study reveals a polynomial penalty for adapting to unknown margin parameters in batched nonparametric bandits.
problem Adapting to an unknown margin parameter in batched nonparametric bandits.
method Introduces the regret inflation criterion and develops RoBIN algorithm to achieve optimal regret inflation.
result The optimal regret inflation grows polynomially with the horizon T, characterized by a convex optimization problem.
We prove that the leaves of an inverse mean curvature flow provide a foliation of a future end of a cosmological spacetime under the necessary and sufficent assumptions that satisfies a future mean curvature barrier condition and a strong volume decay condition. Moreover, the flow parameter can be used to d…
For a given Markov process and survival function on , the inverse first-passage time problem (IFPT) is to find a barrier function such that the survival function of the first-passage time is given by . In …
New method uncovers zero entropy in dependent observations after finite samples.
problem Understanding uncertainty reduction in dependent observations.
method Minimum list entropy coupling, greedy algorithm.
result Zero entropy achieved with O(log(1/P_min)) samples for dependent observations.
New CMC existence result for expanding cosmological spacetimes.
problem Establishing a new constant mean curvature (CMC) existence result for cosmological spacetimes.
method Construction of barriers in the support sense and asymptotic limit of mean curvature flow.
result The existence of a CMC Cauchy surface in expanding cosmological spacetimes.
New symplectic barriers found in ball embeddings.
problem Existence of symplectic embeddings with intersections.
method Proving obligatory intersections with symplectic planes.
result Existence of symplectic barriers in ball embeddings.
This work refines claims about neural network connectivity, showing that simultaneous linear connectivity is possible under certain conditions.
problem Neural networks' loss landscapes are non-convex due to permutation symmetries, leading to high loss barriers between permuted networks.
method The authors introduce and analyze three claims of increasing strength regarding the connectivity of neural networks, focusing on permutations that align networks.
result The authors provide evidence that strong linear connectivity may be possible under certain conditions, specifically when interpolating among three networks of increasing width.
The paper studies how convex surfaces shrink under mean curvature flow with a free boundary.
problem Mean curvature flow of convex surfaces with a free boundary on convex barriers.
method Introduced a new perturbation argument to establish convexity and pinching estimates.
result The flow contracts a sufficiently convex surface to a point in finite time, asymptotic to a half-sphere.
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.
We prove the existence and uniqueness of radial graphs over a given domain of having boundary on the sphere and whose mean curvature at every point equals a prescribed positive function satisfying suitable barrier-type and monotonicity conditions.