American options can be equivalent to European options under certain conditions.
problem Determining when American options can be simplified to European options.
method Using methods from Jourdain and Martini, Chrsitensen, and convex duality.
result A first step towards verifying representability of American options.
The paper values perpetual callable American volatility options using a mean-reverting volatility model.
problem Valuation of callable American volatility put options.
method Modeling volatility dynamics as a mean-reverting 3/2 process and proposing a pricing formula.
result The value of perpetual callable American volatility put options is discussed under given conditions.
We consider the pricing of American put options in a model-independent setting: that is, we do not assume that asset prices behave according to a given model, but aim to draw conclusions that hold in any model. We incorporate market information by supposing that the prices of European options are known. In this setting…
Researchers find a way to price American options without relying on specific asset price models.
problem Determining the upper bound on the price of American options under model uncertainty.
method Using martingale optimal transport problem to describe model uncertainty and proving that optimal exercise schemes must be nonrandomized under certain conditions.
result The price upper bound and its relaxed version coincide under suitable convexity conditions, removing the need for the model-free price upper bound to be nonrandomized.
Paper proves minimax theorem for American options in incomplete markets.
problem Characterizing arbitrage-free prices of American options in incomplete markets.
method Sufficient conditions guaranteeing minimax theorem validity for lower Snell envelope.
result Minimax results reveal unexpected connection to density process path properties.
ETCNN uses neural networks to price American options accurately.
problem Accurately pricing American options with inequality constraints.
method ETCNN framework solving BSM equations with exact terminal condition.
result ETCNN achieves high accuracy and robustness across various scenarios.
The Volterra Heston model is used to price American options.
problem Pricing American options in the Volterra Heston model.
method Kernel-based approximations and simulation techniques.
result Convergence of American option prices in approximating models to the Volterra Heston model.
Paper examines floating exercise boundaries for American options in time-inhomogeneous models.
problem Floating exercise boundaries in time-inhomogeneous models with negative interest rates or yields.
method Semi-analytical approach for pricing American options.
result Specialized pricing methodologies are required for models with floating exercise boundaries.
This paper studies the parabolic free boundary problem arising from pricing American-style put options on an asset whose index follows a geometric Brownian motion process. The contribution is to propose a condition for that the early exercise boundary is a convex function.
Pricing bonus certificates and barrier products uses efficient interpolation and stochastic modeling.
problem Pricing bonus certificates and barrier products with American conditions.
method Efficient interpolation for European conditions, stochastic modeling for American conditions.
result Pricing can be done without stochastic modeling within a certain accuracy range.
The paper prices options using a novel finite element method.
problem Pricing European and American options under the Heston model.
method Discontinuous Galerkin finite element method (dGFEM) with interior penalty and Rannacher smoothing.
result Efficient and accurate pricing of options, demonstrated through comparisons and experiments.
We derive error estimates for multinomial approximations of American options in a multidimensional jump--diffusion Merton's model. We assume that the payoffs are Markovian and satisfy Lipschitz type conditions. Error estimates for such type of approximations were not obtained before. Our main tool is the strong approxi…
This paper compares LSM and ANN/GBM for pricing American put options under a complex model.
problem Pricing American put options using advanced techniques.
method Least-Squares Monte Carlo (LSM) and Artificial Neural Network (ANN) and Gradient Boosted Machine (GBM) Trees.
result LSM outperforms ANN and GBM in pricing American put options.
Binomial tree methods (BTM) and explicit difference schemes (EDS) for the variational inequality model of American options with time dependent coefficients are studied. When volatility is time dependent, it is not reasonable to assume that the dynamics of the underlying asset's price forms a binomial tree if a partitio…
In this paper, we study the valuation of American type derivatives in the stochastic volatility model of Barndorff-Nielsen and Shephard (2001). We characterize the value of such derivatives as the unique viscosity solution of an integral-partial differential equation when the payoff function satisfies a Lipschitz condi…
Compact method for option pricing under jump-diffusion models.
problem Pricing European and American options with jumps.
method Compact finite difference method using Crank-Nicolson Leap-Frog scheme.
result Fourth-order convergence rate achieved with smoothing operators.
This paper develops methods for pricing American Parisian options under general Markov models.
problem Pricing American Parisian options with various types and payoff functions.
method General approaches using CTMC approximation for time-inhomogeneous Markov models, including state augmentation and variational inequalities.
result Efficient algorithms for pricing American Parisian options confirmed with numerical experiments.
Paper addresses stability in multi-asset American option pricing.
problem Stability in multi-asset American option pricing problems.
method Semi-discretization approach followed by full discretization.
result Stability conditions found for numerical solution.
We prove that the perpetual American put option price of level dependent volatility model with compound Poisson jumps is convex and is the classical solution of its associated quasi-variational inequality, that it is C2 except at the stopping boundary and that it is C1 everywhere (i.e. the smooth pasting conditio…
A new method uses Chebyshev polynomials for American option pricing.
problem Pricing American options efficiently and accurately.
method Dynamic Chebyshev interpolation in time-stepping, offline computation of moments, online approximation.
result The method delivers fast convergence and efficiency gains compared to existing methods.
Characterization of the American put option price is still an open issue. From the beginning of the nineties there exists a non-closed formula for this price but nontrivial numerical computations are required to solve it. Strong efforts have been done to propose methods more and more computationally efficient but most …
Conditional Leibniz Derivative Estimation reduces variance in stochastic models.
problem Estimating derivatives in stochastic models with discontinuous sample performance.
method Combining push-out likelihood ratio method with Leibniz integral rules.
result Conditional Leibniz estimator reduces variance and is easy to implement.
The paper analyzes perpetual American options with asset-dependent discounting.
problem Optimal stopping problem for perpetual American options with varying discount rates.
method Analyzes the convexity of the value function, determines stopping regions, and proves HJB equation.
result Identifies the form of the value function and proves put-call symmetry.
American options are financial instruments that can be exercised at any time before expiration. In this paper we study the problem of pricing this kind of derivatives within a framework in which some of the properties --volatility and dividend policy-- of the underlaying stock can change at a random instant of time, bu…
A new method for calibrating American options is tested and found to be reliable in some scenarios but not in others.
problem Calibrating American options for model accuracy.
method De-Americanization method, based on simplifications.
result De-Americanization performs well in some scenarios but can lead to large errors in others.
Continuous-time random walks are a well suited tool for the description of market behaviour at the smallest scale: the tick-to-tick evolution. We will apply this kind of market model to the valuation of perpetual American options: derivatives with no maturity that can be exercised at any time. Our approach leads to opt…
Deep learning method solves American options with free boundary using Landau transformation.
problem Solving American options with a free boundary using deep learning.
method Landau transformation, dual solution framework, auxiliary function, feed forward deep neural network (DNN).
result Deep learning method efficiently prices options with early exercise features.
Study on pricing American Exchange options using Lévy processes.
problem Pricing American Exchange options driven by Lévy processes.
method Represented American Exchange options as European options plus early exercise premium; studied properties of free boundary and provided an approximative formula.
result Developed an approximative formula for American Exchange options.
Study Markov cubature rules for polynomial processes.
problem Tractability of path-dependent tasks in polynomial process models.
method Discretizations using finite state Markov processes with moment matching conditions.
result Markov cubature rules aid American option pricing.
Analyzes American option pricing with fractional derivatives.
problem Characterizing American option prices under modified models.
method Uses fractional partial differential equations and approximation techniques.
result Proves convexity of American put prices and tail index impact.
Study solves perpetual American option pricing using variational inequality and difference equation.
problem Pricing perpetual American options.
method Proved maximum principle and uniqueness for variational inequality, provided existence and uniqueness for difference equation, and proved convergence of difference equation solution to variational inequality solution.
result Solution to difference equation converges to viscosity solution of variational inequality, showing perpetual American option prices converge as maturity approaches infinity.
Maximizes American put price bounds using European put prices.
problem Finding upper bounds for American put prices.
method Model-free approach using European put prices and martingale transport.
result Derives a model with maximal American put price.
Unified framework for hedging American options, including shorting.
problem Generalizing hedging principles to American options, especially shorting.
method Unified framework, enlarging probability spaces, converting shorted options to European options.
result Unified FTAP and hedging dualities for American options, including shorting.
Establish C^{1,2} regularity of American value functions in Heston model
problem Regularity of American put options in Heston model
method PDE techniques
result C^{1,2} regularity in exercise domain and smooth-fit principle
Paper quantifies value of American option flexibility in uncertain models.
problem Value of American option flexibility in uncertain models.
method Identifies supremum price bound using hedging strategy with European call options.
result Quantifies potential value of American option flexibility.
The paper prices American-style Parisian down-and-in call options using the Black-Scholes framework.
problem Pricing American-style Parisian down-and-in call options under the Black-Scholes framework.
method Developed a simple analytical solution using the moving window technique.
result Obtained a new formula for pricing American-style Parisian down-and-in call options in terms of four double integrals.
Perpetual American options are financial instruments that can be readily exercised and do not mature. In this paper we study in detail the problem of pricing this kind of derivatives, for the most popular flavour, within a framework in which some of the properties |volatility and dividend policy| of the underlying stoc…
Deep neural operators learn complex probabilistic models efficiently.
problem Learning complex probabilistic models with global Lipschitz conditions.
method Deep neural-operator framework under global Lipschitz conditions.
result Explicit network-size bounds for universal approximation of probabilistic models.
Study compares three splitting methods for American option valuation.
problem Valuation of American options using numerical methods.
method Three splitting methods: explicit payoff, Ikonen-Toivanen, Peaceman-Rachford.
result Temporal accuracy of splitting methods compared to penalty approach.
Optimizes American option exercise timing with discounted Brownian bridge model.
problem Optimizing American option exercise timing under special market conditions.
method Modeling terminal price as a Brownian bridge with future information disclosure and discount factor inclusion.
result Characterization and numerical computation of optimal stopping boundary with discount factor.
Researchers derive a new equation for valuing American options.
problem Valuation and hedging of American options on dividend-paying assets.
method Derive a stochastic balance equation for the value function and its gradient.
result The derived equation uniquely solves the valuation problem.
MNN improves American call option pricing accuracy.
problem Inaccurate valuation of American call options.
method Modular Neural Network (MNN) model.
result MNN model outperforms traditional models and FNN.
Clarifies conflicting results on hedging American options under model uncertainty.
problem Conflicting results on the cost of the cheapest super-replicating strategy for American options.
method Shows that Bayraktar et al. do not search over a sufficiently rich class of models.
result The cost of the cheapest super-replicating strategy can strictly exceed the highest model-based price under model uncertainty.
Analyzes American swaption pricing in LR model, solving optimal stopping problem.
problem Analyzes American swaption pricing in LR model.
method Analyzes American swaption pricing in LR model, solving optimal stopping problem.
result Characterizes optimal stopping boundary and obtains arbitrage-free price.
Study applies HRP to Latin American markets, showing smoother risk-return profile.
problem Lack of empirical analyses of HRP in Latin American markets.
method Hierarchical Risk Parity (HRP) with hierarchical clustering and recursive bisection.
result HRP portfolio outperforms Max Sharpe portfolio in NUAM markets, with smoother risk-return profile.
In this paper, we present a new method for calculating the limit of early exercise boundary at expiry. We price American style of general derivative using a formula expressed as a sum of the value of European style of derivative and so called American premium. We use the latter expression to calculate an analytic formu…
New framework identifies hidden risks and optionality in American options.
problem Underestimation of flexibility and convexity in early-exercise features.
method Introducing stochasticity into underlying determinants to quantify hidden risks and optionality.
result Remedies conventional pricing systems that underestimate optionality.
Paper develops semi-analytic method for American options in time-dependent jump-diffusion models.
problem Pricing American options in models with time-dependent and exponential jumps.
method Generalizes existing methods for barrier and American options to handle arbitrary time dependencies and solves the problem through algebraic and Fredholm-Volterra equations.
result Presents a semi-analytic solution for American options in time-dependent jump-diffusion models with exponential jumps.