The purpose of this paper is to construct the early exercise boundary for a class of nonlinear Black--Scholes equations with a nonlinear volatility depending on the option price. We review a method how to transform the problem into a solution of a time depending nonlinear parabolic equation defined on a fixed domain. R…
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48 results for “early-exercise”
Pricing methods for -quantile and perpetual early exercise options based on Spitzer identitiesq-fin.CP
New pricing methods for -quantile and early-exercise options using Spitzer identities.
problem Pricing perpetual Bermudan and American options and -quantile options.
method Based on Spitzer identities for general Lévy processes and Wiener-Hopf method.
result Direct calculation of the optimal exercise barrier for early-exercise options.
In this paper we generalize and analyze the model for pricing American-style Asian options due to (Hansen and Jorgensen 2000) by including a continuous dividend rate and a general method of averaging of the floating strike. We focus on the qualitative and quantitative analysis of the early exercise boundary. The fi…
Enhanced SFP-FCC method for early-exercise options pricing and hedging.
problem Pricing and hedging early-exercise options under Lévy processes.
method Combines SFP method with Filon-Clenshaw-Curtis (FCC) rules.
result Retains global spectral convergence rate and fast error convergence.
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…
In this paper we present qualitative and quantitative comparison of various analytical and numerical approximation methods for calculating a position of the early exercise boundary of the American put option paying zero dividends. First we analyze their asymptotic behavior close to expiration. In the second part of the…
Paper defines when early exercise of American options is optimal under negative rates.
problem Determining optimal exercise times for American options with negative interest rates.
method Developed a new integral equation to price options and find exercise boundaries under negative rates, using modified fixed point method.
result Successfully developed and validated a new algorithm for pricing American options under negative rates.
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.
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.
The purpose of this paper is to analyze and compute the early exercise boundary for a class of nonlinear Black--Scholes equations with a nonlinear volatility which can be a function of the second derivative of the option price itself. A motivation for studying the nonlinear Black--Scholes equation with a nonlinear vola…
The purpose of this survey chapter is to present a transformation technique that can be used in analysis and numerical computation of the early exercise boundary for an American style of vanilla options that can be modelled by class of generalized Black-Scholes equations. We analyze qualitatively and quantitatively the…
Using a fast numerical technique, we investigate a large database of investor suboptimal non-exercise of short maturity American call options on dividend-paying stocks listed on the Dow Jones. The correct modelling of the discrete dividend is essential for a correct calculation of the early exercise boundary as confirm…
A simple and efficient numerical method for pricing discretely monitored early-exercise optionsq-fin.CP
A fast method for pricing various financial options.
problem Efficient pricing of discretely monitored early-exercise options.
method A quadrature technique-based method using elementary calculations and a fixed grid.
result Convergence rate of and complexity of .
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…
A new method for pricing exchange options under stochastic volatility and jumps.
problem Pricing European and American exchange options with stochastic volatility and jumps.
method Equivalent martingale measure, numeraire choice, integral transforms, Kolmogorov backward equation, integral equations.
result Reduced exchange option pricing to a one-dimensional problem of a call option.
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…
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.
In this paper we analyze American style of floating strike Asian call options belonging to the class of financial derivatives whose payoff diagram depends not only on the underlying asset price but also on the path average of underlying asset prices over some predetermined time interval. The mathematical model for the …
We analyze and calculate the early exercise boundary for a class of stationary generalized Black-Scholes equations in which the volatility function depends on the second derivative of the option price itself. A motivation for studying the nonlinear Black Scholes equation with a nonlinear volatility arises from option p…
Deep learning solves complex financial option pricing problems.
problem High-dimensional optimal stopping problems in financial derivatives pricing.
method Deep learning algorithm for approximating optimal exercise strategies and option prices.
result Effective in pricing many high-dimensional American and Bermudan options.
New deep learning solver for high-dimensional derivative pricing.
problem High-dimensional derivatives pricing problems.
method Combines deep learning with least square regression for backward SDE solving.
result Accurate and efficient pricing of complex derivatives.
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.
In this paper, we extend the 3/2-model for VIX studied by Goard and Mazur (2013) and introduce the generalized 3/2 and 1/2 classes of volatility processes. Under these models, we study the pricing of European and American VIX options and, for the latter, we obtain an early exercise premium representation using a free-b…
This paper applies an algorithm for the convolution of compactly supported Legendre series (the CONLeg method) (cf. Hale and Townsend 2014a), to pricing/hedging European-type, early-exercise and discrete-monitored barrier options under a Levy process. The paper employs Chebfun (cf. Trefethen et al. 2014) in computation…
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.
This work addresses the problem of pricing American basket options in a multivariate setting, which includes among others, the Bachelier and the Black-Scholes models. In high dimensions, nonlinear partial differential equation methods for solving the problem become prohibitively costly due to the curse of dimensionalit…
Hermite Polynomial-based Valuation of American Options with General Jump-Diffusion Processesq-fin.CP
New method uses Hermite polynomials for American option valuation.
problem Valuation of American options with complex jump-diffusion dynamics.
method Hermite polynomial expansions of transition density and early exercise premium.
result Converging approximations to true option prices and exercise boundaries.
Valuation and parity formulas for both European-style and American-style exchange options are presented in a general financial model allowing for jumps, possibility of default and "bubbles" in asset prices. The formulas are given via expectations of auxiliary probabilities using the change-of-numeraire technique. Exten…
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.
A Hybrid LSMC-PDE Method for Bermudan Option Pricing under the Gatheral Double Mean-Reverting Modelq-fin.PR
Hybrid LSMC-PDE method for Bermudan options under GDMR model.
problem Pricing Bermudan options under the GDMR model.
method Adapted Hybrid LSMC-PDE framework, combining Monte Carlo and PDE methods.
result Hybrid approach yields more accurate and lower error estimates than plain LSMC.
Numerical method for pricing exchange options with stochastic volatility and jumps.
problem Pricing exchange options under stochastic volatility and jump-diffusion dynamics.
method Method of lines (MOL) approach to simplify and solve the PDEs.
result Characterization of near-maturity American exchange option boundary and impact of model parameters.
Deep Hedging Bermudan Swaptionsq-fin.CP
Paper proposes a deep hedging method for Bermudan swaptions to manage residual profit and loss.
problem Real-world market conditions differ from ideal assumptions in traditional hedging methods, leading to residual profit and loss.
method Deep hedging framework applied to Bermudan swaptions, allowing flexible risk measures and hedge strategies.
result Effective residual profit and loss management demonstrated through numerical analysis.
Valuing FF contracts in time-dependent models
problem Valuing American options and Flexible Forwards contracts
method Recursive Riccati solution and Volterra equation
result FF contracts priced faster than traditional methods
We generalize the primal-dual methodology, which is popular in the pricing of early-exercise options, to a backward dynamic programming equation associated with time discretization schemes of (reflected) backward stochastic differential equations (BSDEs). Taking as an input some approximate solution of the backward dyn…
A neural network solves Black-Scholes PDE for option pricing with uncertainty quantification.
problem Solving the Black-Scholes equation for option pricing with uncertainty.
method Physics-informed neural network (PINN) that embeds BS operator and conditions, handles early exercise via relaxation, and uses anchored-ensemble fine-tuning for uncertainty quantification.
result The method achieves low errors and accurate predictions for European and American options, outperforming data-driven baselines.
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 …
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…
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…
In the paper, we propose a new calculation scheme for American options in the framework of a forward backward stochastic differential equation (FBSDE). The well-known decomposition of an American option price with that of a European option of the same maturity and the remaining early exercise premium can be cast into t…
We consider the problem of ESO valuation in continuous time. In particular, we consider models that assume that an appropriate random time serves as a proxy for anything that causes the ESO's holder to exercise the option early, namely, reflects the ESO holder's job termination risk as well as early exercise behaviour.…
This paper studies the valuation of a class of default swaps with the embedded option to switch to a different premium and notional principal anytime prior to a credit event. These are early exercisable contracts that give the protection buyer or seller the right to step-up, step-down, or cancel the swap position. The …
The paper uses deep learning to efficiently price Bermudan swaptions.
problem Pricing Bermudan swaptions efficiently and accurately.
method Combines differential machine learning, Monte Carlo simulation, and joint learning.
result Improves efficiency and accuracy in pricing Bermudan swaptions.
We describe a model for evolving commodity forward prices that incorporates three important dynamics which appear in many commodity markets: mean reversion in spot prices and the resulting Samuelson effect on volatility term structure, decorrelation of moves in different points on the forward curve, and implied volatil…
The paper adjusts stock and strike prices for dividends after maturity in stock call pricing.
problem Inconsistent pricing of European calls with dividends after maturity.
method Extension of the Black-Scholes formula to include dividends after maturity.
result Model-consistent pricing of calls over all maturities with dividends after maturity.
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.
Quantum computing speeds up Bermudan option pricing.
problem Efficient pricing of financial derivatives, especially Bermudan options.
method Quantum amplitude estimation combined with Chebyshev interpolation.
result Quadratic speed-up over classical methods.
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.
The non-Markovian nature of rough volatility processes makes Monte Carlo methods challenging and it is in fact a major challenge to develop fast and accurate simulation algorithms. We provide an efficient one for stochastic Volterra processes, based on an extension of Donsker's approximation of Brownian motion to the f…