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…
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48 results for “moving barriers”
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.
The thesis explores prediction games with different opponents and moves, revealing intrinsic barriers and efficient algorithms.
problem Understanding and designing efficient algorithms for prediction games with various opponents and move orders.
method Geometric insights into three types of prediction games: general learning task, prediction with expert advice, and online convex optimization.
result Revealed intrinsic barriers and developed computationally efficient learning algorithms with strong theoretical guarantees.
Stochastic Spot/Volatility Correlation in Stochastic Volatility Models and Barrier Option Pricingq-fin.PR
Most models for barrier pricing are designed to let a market maker tune the model-implied covariance between moves in the asset spot price and moves in the implied volatility skew. This is often implemented with a local volatility/stochastic volatility mixture model, where the mixture parameter tunes that covariance. T…
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.
We say that a topologically embedded 3-sphere in a smoothing of Euclidean 4-space is a barrier provided, roughly, no diffeomorphism of the 4-manifold moves the 3-sphere off itself. In this paper we construct infinitely many one parameter families of distinct smoothings of 4-space with barrier 3-spheres. \par The existe…
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.
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.
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.
A new model adds stochastic spot/volatility correlation to Heston model for better exotic pricing.
problem Improving exotic option pricing in foreign exchange markets.
method Developed a Double Heston model with stochastic spot/volatility correlation, an affine model.
result The new model increases prices of out-of-the-money knockout options and one touch options.
Develops a new method for pricing barrier options in time-dependent Heston model.
problem Pricing barrier options in a time-dependent Heston model with stochastic volatility.
method General Integral Transforms (GIT) method for a two-dimensional integral representation.
result Shows that the GIT method can be extended to two drivers with inhomogeneous correlation.
Approximating Functional of Local Martingale Under the Lack of Uniqueness of Black-Scholes PDEq-fin.PR
When the underlying stock price is a strict local martingale process under an equivalent local martingale measure, Black-Scholes PDE associated with an European option may have multiple solutions. In this paper, we study an approximation for the smallest hedging price of such an European option. Our results show that a…
Paper overcomes sample size barrier in reinforcement learning with generative models.
problem Sample efficiency in reinforcement learning with generative models.
method Developed two algorithms to certify minimax optimality of sample complexity.
result Achieved minimax-optimal guarantees for a wide range of sample sizes.
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.
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…
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.
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…
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…
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.
Credit Calibration with Structural Models: The Lehman case and Equity Swaps under Counterparty Riskq-fin.PR
In this paper we develop structural first passage models (AT1P and SBTV) with time-varying volatility and characterized by high tractability, moving from the original work of Brigo and Tarenghi (2004, 2005) [19] [20] and Brigo and Morini (2006)[15]. The models can be calibrated exactly to credit spreads using efficient…
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.
We introduce a globally-convergent algorithm for optimizing the tree-reweighted (TRW) variational objective over the marginal polytope. The algorithm is based on the conditional gradient method (Frank-Wolfe) and moves pseudomarginals within the marginal polytope through repeated maximum a posteriori (MAP) calls. This m…
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.
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.
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…
Mode connectivity framework shows resilience to model differences.
problem Investigating the limits of mode connectivity in extreme cases.
method Empirically examines mode connectivity between differently trained models.
result The procedure is resilient to changes in model training or initialization.
Convergence and cluster structures in EU area according to fluctuations in macroeconomic indicesq-fin.GN
The cluster analysis methods are used in order to perform a comparative study of 15 EU countries in relation with the fluctuations of some basic macroeconomic indicators. The statistical distances between countries are calculated for various moving time windows, and the time variation of the mean statistical distance i…
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.
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.
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.
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.
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…
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…
We derive a forward equation for arbitrage-free barrier option prices, in terms of Markovian projections of the stochastic volatility process, in continuous semi-martingale models. This provides a Dupire-type formula for the coefficient derived by Brunick and Shreve for their mimicking diffusion and can be interpreted …
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.
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…
Bayesian method synthesizes barrier certificates for unknown systems with latent states.
problem Certifying safety in systems with unknown dynamics and latent states.
method Bayesian inference with Metropolis-Hastings sampler and sum-of-squares program.
result Probabilistic validity of barrier certificates for unknown systems.
A Walk with SGDstat.ML
SGD explores loss surface by bouncing between valley walls, aiding generalization.
problem Understanding SGD's role in over-parametrized DNNs.
method Interpolating loss surface between consecutive SGD iterations, tracking metrics.
result SGD moves in valley-like regions, jumping between walls at a height above the valley floor.
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.
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…
Develops a framework for stuck knots with rigid constraints and invariants.
problem Rigidity constraints on knot diagrams restrict allowable isotopies.
method Formalizes stuck crossings as rigid configurations, introduces unstick move, and constructs invariants.
result Rigidity contributes independent information even when knot type remains fixed.
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.
Proposes a new framework for invariant quadratic P&L predictions in option books.
problem Inconsistent second-order P&L predictions across different factor parameterizations.
method Local, model-agnostic framework using covariant Hessian defined by an affine connection.
result Coordinate-invariant quadratic P&L predictions that match desk targets.
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…
We use the Gromov-Witten invariants and a nonsqueezing theorem by the author to affirm a conjecture by P.Biran on the Lagrangian barriers.