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…
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48 results for “American derivatives”
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.
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.
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…
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…
The paper calculates XVA for complex basket derivatives using machine learning.
problem Computing XVA for American basket derivatives with multiple underlying assets.
method The approach combines machine learning (Gaussian Process Regression) with numerical techniques (control variates) to handle high-dimensional control problems.
result The proposed machine learning methods effectively compute XVA for basket derivatives.
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…
In this article, a compact finite difference method is proposed for pricing European and American options under jump-diffusion models. Partial integro-differential equation and linear complementary problem governing European and American options respectively are discretized using Crank-Nicolson Leap-Frog scheme. In pro…
We consider the problem of finding a model-free upper bound on the price of an American put given the prices of a family of European puts on the same underlying asset. Specifically we assume that the American put must be exercised at either or and that we know the prices of all vanilla European puts with th…
Paper improves American option valuation in complex models.
problem Valuation of American options in time-dependent jump-diffusion models.
method Integral equations and characteristic functions for explicit exercise boundary determination.
result Efficient and accurate pricing method for American options in various models.
Deep learning method for pricing and hedging American-style options.
problem Pricing and hedging American-style options with high accuracy.
method Computes optimal stopping policy, derives bounds, calculates point estimate and confidence intervals, constructs hedging strategy.
result Highly accurate prices and dynamic hedging strategies with small replication errors.
A make-your-mind-up option is an American derivative with delivery lags. We show that its put option can be decomposed as a European put and a new type of American-style derivative. The latter is an option for which the investor receives the Greek Theta of the corresponding European option as the running payoff, and de…
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.
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.
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.
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.
Study geometric step options with jumps, deriving pricing equations and characterizations.
problem Pricing geometric step options in markets with jumps.
method Symmetry and parity relations, partial integro-differential equations, ordinary integro-differential equations.
result Derive semi-analytical pricing results for geometric step options.
This paper analyzes model risk in American put options using Heston volatility model.
problem Model risk in optimal exercise of American put options.
method Benchmark methodology of Hull and Suo [2002], Heston stochastic volatility model, numerical finite difference methods.
result Optimal exercise behavior is influenced by stochastic volatility dynamics and return-volatility correlation, creating model risk.
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.
Researchers find the optimal exercise time for American options using a specific type of diffusion process.
problem Finding the optimal time to exercise American options with a time-dependent Ornstein-Uhlenbeck process.
method Optimal stopping problem, probabilistic arguments, non-linear Volterra-type integral equation, Picard iteration algorithm.
result They derive a non-linear Volterra-type integral equation and prove the exercise boundary's Lipschitz continuity and differentiability almost everywhere.
New method for pricing and hedging options in risky markets.
problem Pricing and hedging derivatives in markets with equivalent local martingale measures not existing.
method Introduces a new superhedging duality for American options in a general market setting.
result Answers a question raised by Fernholz, Karatzas, and Kardaras about pricing American options.
European options can be priced by solving parabolic partial(-integro) differential equations under stochastic volatility and jump-diffusion models like Heston, Merton, and Bates models. American option prices can be obtained by solving linear complementary problems (LCPs) with the same operators. A finite difference di…
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.
The target of this paper is to establish the bid-ask pricing frame work for the American contingent claims against risky assets with G-asset price systems (see \cite{Chen2013b}) on the financial market under Knight uncertainty. First, we prove G-Dooby-Meyer decomposition for G-supermartingale. Furthermore, we consider …
Develops trinomial models using cubature methods for financial derivative pricing.
problem Pricing financial derivatives in complex stochastic market models.
method Cubature methods applied to Wiener space for constructing trinomial models.
result Numerical solutions compare favorably with Black-Scholes model.
A new method solves American put options with high accuracy and speed.
problem Solving American put options with high accuracy and speed.
method Adaptive fourth-order Runge-Kutta-Fehlberg method coupled with a fourth-order compact scheme.
result The method provides a more accurate solution and better performance in terms of computational speed.
We derive explicit formulas for time decay, for the European call and put options at expiry, and use them to calculate analytical approximations to the price of the American put and early exercise boundary near expiry. We show that for many families of non-Gaussian processes used in empirical studies of financial marke…
Simultaneous upper and lower bounds of American-style option prices with hedging via neural networksq-fin.CP
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.
Researchers calculate the price of a perpetual put option in Lévy models.
problem Calculating the price of a perpetual American put option in Lévy models.
method Derive the explicit price using geometric spectrally negative Lévy processes and optimal threshold.
result The optimal exercise time is the first epoch when the asset price drops below an optimal threshold.
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…
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.
Efficient and Accurate Calibration to FX Market Skew with Fully Parameterized Local Volatility Modelq-fin.PR
Model accurately calibrates FX market skew for exotic options.
problem Inconsistent prices from different models for FX derivatives.
method Fully parameterized local volatility model with numerical methods.
result Model provides reliable prices for daily trading.
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…
Near-Maturity Asymptotics of Critical Prices of American Put Options under Exponential Lévy Modelsq-fin.MF
Study near-maturity convergence rates of American put prices in Lévy models.
problem Analyzing convergence rates of optimal exercise prices in Lévy models.
method Examined two settings: jumps of unbounded and bounded variation, deriving near-maturity expansions.
result Near-maturity convergence rate of optimal exercise price is of order √(T-t).
On perpetual American put valuation and first-passage in a regime-switching model with jumpsq-fin.PR
In this paper we consider the problem of pricing a perpetual American put option in an exponential regime-switching Lévy model. For the case of the (dense) class of phase-type jumps and finitely many regimes we derive an explicit expression for the value function. The solution of the corresponding first passage problem…
Enhances option pricing for American-style options using JDOI method.
problem Pricing American-style options efficiently under stochastic volatility.
method Extends DOI variance reduction technique to Lévy dynamics, combining with LSMC.
result Strong variance reduction in option pricing compared to standard LSMC.
This paper surveys options pricing under arithmetic Brownian motion and derives formulas for various types of options.
problem The use of arithmetic Brownian motion in finance is not widely adopted.
method Risk-neutral valuation and derivation of formulas for European options under three types of underlying assets.
result Derivation of formulas for European options and partial differential equations for American options.
A Path Integral Way to Option Pricingcond-mat.stat-mech
An efficient computational algorithm to price financial derivatives is presented. It is based on a path integral formulation of the pricing problem. It is shown how the path integral approach can be worked out in order to obtain fast and accurate predictions for the value of a large class of options, including those wi…
Study pricing of American put options with stochastic interest rate and finite maturity.
problem Pricing American put options with stochastic interest rate and finite maturity.
method Applied stochastic calculus and Ito's lemma to derive the option value's formula and optimal exercise boundary.
result Existence and parametrisation of the optimal exercise boundary for the Vasicek model.
In this paper, we investigate the generalization of the Call-Put duality equality obtained in [1] for perpetual American options when the Call-Put payoff is replaced by . It turns out that the duality still holds under monotonicity and concavity assumptions on . The specific analytical form of the …
This paper develops a novel numerical method for pricing American options in a two-asset jump-diffusion model.
problem Pricing American options under correlated two-asset jump-diffusion models using finite difference methods often fails to preserve monotonicity and accurately discretize jump integrals.
method Introduces a novel monotone integration scheme to solve 2-D Partial Integro-Differential Equations (PIDEs) efficiently and accurately.
result The proposed method ensures convergence to the viscosity solution of the variational inequality and is both -stable and consistent.
Fast ML framework for derivative valuation from volatility surfaces.
problem Derivative valuation from complex volatility surfaces.
method Parameterized SVI model, synthetic market scenarios, Gaussian Process Regressor.
result Very accurate and fast (3-4 orders of magnitude) derivative valuations.
Representation of Exchange Option Prices under Stochastic Volatility Jump-Diffusion Dynamicsq-fin.MF
The article provides representations of exchange option prices under SVJD dynamics.
problem Modeling and pricing exchange options under stochastic volatility and jumps.
method Develops representations for European and American exchange options using SVJD dynamics and equivalent martingale measures.
result Derives integro-partial differential equations and representations for exchange option prices.
The paper extends Strassen's theorem to include biased martingales for American options.
problem Existence of martingales for arbitrage-free prices of American options.
method Derives an extension of Strassen's theorem linking biased martingales to strengthened convex order.
result Characterizes the strengthened convex order through integrals with respect to compensated Poisson processes.
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.
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.
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.
The theme in this paper is the recombining binomial tree to price American put option when the underlying stock follows constant elasticity of variance(CEV) process. Recombining nodes of binomial tree are decided from finite difference scheme to emulate CEV process and the tree has a linear complexity. Also it is deriv…