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.
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.
Study bounds for prices of European and American options with optional termination.
problem Bounding prices of options with potential termination.
method Duality results linking upper prices of vulnerable options to American options with constrained exercise times.
result Linking upper prices of vulnerable options to American options and game options.
We price and hedge American options robustly in continuous time.
problem Pricing and hedging American options in continuous time with model uncertainty.
method Assumes continuous semimartingale asset prices and closed convex constraints on volatility. Proves robust pricing-hedging duality and identifies American options as European options on an enlarged space.
result We prove robust pricing-hedging duality and show it holds against richer models with dynamic trading of European options.
In this paper, we price American-style Parisian down-and-in call options under the Black-Scholes framework. Usually, pricing an American-style option is much more difficult than pricing its European-style counterpart because of the appearance of the optimal exercise boundary in the former. Fortunately, the optimal exer…
New option pricing formulas for American and Bermudan options.
problem Traditional option pricing models assume constant volatility and interest rate.
method Relaxing assumptions, using square root of Brownian motion, providing closed-form formulas.
result Simple, closed-form pricing formulas for American and Bermudan options.
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 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.
This paper investigates analytic properties of American option prices under the finite moment log-stable (FMLS) model. Under this model the price of American options is characterised by the free boundary problem of a fractional partial differential equation (FPDE) system. Using the technique of approximation we prove t…
A variational inequality for pricing the perpetual American option and the corresponding difference equation are considered. First, the maximum principle and uniqueness of the solution to variational inequality for pricing the perpetual American option are proved. Then the maximum principle, the existence and uniquenes…
The paper uses LSMC to price capped American options with time-dependent caps.
problem Pricing American options with time-capped features.
method Least Squares Monte Carlo (LSMC) method.
result The LSMC method converges to the true price as discretization step and number of trajectories approach limits.
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.
An analytic method for pricing American call options is provided; followed by an empirical method for pricing Asian call options. The methodology is the pricing theory presented in "A Modern Theory of Random Variation", by Patrick Muldowney, 2012.
Our goal here is to discuss the pricing problem of European and American options in discrete time using elementary calculus so as to be an easy reference for first year undergraduate students. Using the binomial model we compute the fair price of European and American options. We explain the notion of Arbitrage and the…
The purpose of this note is to reconcile two different results concerning the model-free upper bound on the price of an American option, given a set of European option prices. Neuberger (2007, `Bounds on the American option') and Hobson and Neuberger (2016, `On the value of being American') argue that the cost of the c…
Paper proposes an alternative method to price American options using HJM approach.
problem Price American options efficiently and accurately.
method Utilizes HJM technique to model term structure of volatility for equity markets.
result Proposes a new value function, stopping criteria, and stopping time for American options.
This paper uses deep learning to price American options under stochastic volatility.
problem Pricing American options with a time-varying exercise boundary under the Heston model.
method Coupled PINNs with curriculum learning and adaptive resampling.
result Demonstrates the effectiveness of the proposed deep learning framework for American option pricing.
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.
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…
KANOP uses KANs to efficiently price American options.
problem Efficiently pricing American options with limited data.
method Combines KANs with LSMC to estimate continuation value.
result KANOP provides more accurate option value estimates.
Two neural network methods solve American-style option pricing and hedging.
problem Solving American-style option pricing and hedging problems efficiently.
method Two novel neural network methods: one series of networks and one global network.
result Simultaneous computation of upper and lower bounds with reduced complexity.
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…
It is well known how to determine the price of perpetual American options if the underlying stock price is a time-homogeneous diffusion. In the present paper we consider the inverse problem, that is, given prices of perpetual American options for different strikes, we show how to construct a time-homogeneous stock pric…
New methods price American options in rough volatility models.
problem Pricing American options under rough volatility.
method Integrating deep-signature and signature-kernel learning into optimal stopping problem solutions.
result Performance comparison in rough Heston and rough Bergomi models.
Efficient method for pricing European and American options using Markov switching stochastic volatility model.
problem Modeling and pricing options under varying volatility and mean-reversion speeds.
method Discrete-time Markov switching stochastic volatility with co-jump model, computationally efficient approach for European options, and conversion to European option pricing for American options.
result Efficient and accurate methods for pricing options, including variance swap analysis.
Deep RNNs compute American option prices and deltas efficiently.
problem Computing prices and deltas of high-dimensional American options.
method Two deep RNNs, one for price and one for delta, learn over spacetime.
result Linear time and constant memory cost compared to feedforward networks.
In this paper we investigate a nonlinear generalization of the Black-Scholes equation for pricing American style call options in which the volatility term may depend on the underlying asset price and the Gamma of the option. We propose a numerical method for pricing American style call options by means of transformatio…
This paper deals with pricing of European and American options, when the underlying asset price follows Heston model, via the interior penalty discontinuous Galerkin finite element method (dGFEM). The advantages of dGFEM space discretization with Rannacher smoothing as time integrator with nonsmooth initial and boundar…
Paper calculates perpetual put option pricing with drawdown cap.
problem Pricing perpetual American put options with drawdown constraints.
method Derives explicit formula using Black-Scholes model and martingale theory.
result Optimal exercise occurs at first drawdown below a threshold.
We consider the super-hedging price of an American option in a discrete-time market in which stocks are available for dynamic trading and European options are available for static trading. We show that the super-hedging price π is given by the supremum over the prices of the American option under randomized models. T…
New method for pricing SOFR futures options, solving both American and Asian exercise styles.
problem Lack of pricing models for SOFR futures options post-LIBOR transition.
method Developed a new version of the GIT method to solve semi-analytically.
result Obtained option prices, exercise boundaries, and Greeks for American and Asian options.
Paper calculates perpetual American put option pricing with drawdown event in Lévy market.
problem Pricing perpetual American put options with a drawdown event in a Lévy market.
method Derives explicit price using geometric Lévy process with downward jumps, optimal stopping rule, and martingale arguments.
result Optimal stopping rule is the first time asset price falls below a specific value.
Study values American passport options in an exponential Lévy model.
problem Valuing an exotic derivative called the American passport option.
method Derived pricing equation using dynamic programming principle and proved viscosity solution.
result Option value is a viscosity solution of variational inequality and is convex.
Research improves pricing of multidimensional American options using neural networks.
problem Pricing multidimensional American options efficiently and accurately.
method Time Deep Gradient Flow (TDGF) method and Deep Galerkin Method (DGM).
result TDGF method achieves high accuracy and faster training than DGM.
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.
AES scheme improves Bermudan and American option pricing for Heston models.
problem Pricing Bermudan and American options under Heston models efficiently.
method AES scheme using non-central chi-square distribution for variance process.
result AES achieves higher accuracy and computational efficiency for Bermudan options.
In this paper an improved Cuckoo Search Algorithm is developed to allow for an efficient and robust calibration of the Heston option pricing model for American options. Calibration of stochastic volatility models like the Heston is significantly harder than classical option pricing models as more parameters have to be …
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.
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.
Novel method uses PDifMPs to price American options more accurately.
problem Inaccurate pricing of American options due to constant drift and volatility assumptions.
method Piecewise diffusion Markov processes (PDifMPs) integrated with continuous dynamics and discrete jumps.
result PDifMPs provide a more accurate reflection of market behaviour in American option pricing.
New method for pricing American options in time-dependent models, improving accuracy and efficiency.
problem Pricing American options in time-dependent models with improved accuracy and efficiency.
method Semi-analytical pricing using a nonlinear Volterra integral equation and numerical methods.
result Improved accuracy and efficiency in pricing American options compared to forward finite difference solvers.
The aim of this study was to develop methods for evaluating the American-style option prices when the volatility of the underlying asset is described by a stochastic process. As part of this problem were developed techniques for modeling the early exercise surface of the American option. These methods of present work a…
The study examines pricing American options with both exogenous and endogenous transaction costs.
problem Pricing American options with transaction costs and liquidity risks.
method Modeling liquidity risks as a mean-reverting process and transaction costs as proportional to trading amount. Two nonlinear PDEs are used to characterize option values. Numerical solution via ADI method and model calibration using maximum likelihood estimation.
result The model incorporating liquidity risks significantly outperforms the Leland model.
In this article we propose a novel approach to reduce the computational complexity of various approximation methods for pricing discrete time American options. Given a sequence of continuation values estimates corresponding to different levels of spatial approximation and time discretization, we propose a multi-level l…
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.
Since most of the traded options on individual stocks is of American type it is of interest to generalize the results obtained in semi-static trading to the case when one is allowed to statically trade American options. However, this problem has proved to be elusive so far because of the asymmetric nature of the positi…
Efficiently prices American options with multiple assets using sparse grids.
problem Pricing American options with multiple underlying assets efficiently.
method Dynamic programming formulation followed by sparse grid interpolation.
result Sparse grids reduce the number of interpolation points and maintain function smoothness.
The Runge-Kutta-Legendre scheme improves pricing American options and other derivatives.
problem Pricing American options and other derivatives with improved accuracy and stability.
method Runge-Kutta-Legendre finite difference scheme applied to Black-Scholes and Heston models.
result Improved convergence and stability compared to existing schemes.