We present three models of stock price with time-dependent interest rate, dividend yield, and volatility, respectively, that allow for explicit forms of the optimal exercise boundary of the finite maturity American put option. The optimal exercise boundary satisfies the nonlinear integral equation of Volterra type. We …
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,695 papers · 148 categories
Trend · papers per month
48 results for “optimal exercise”
We present a novel method for the numerical pricing of American options based on Monte Carlo simulation and the optimization of exercise strategies. Previous solutions to this problem either explicitly or implicitly determine so-called optimal exercise regions, which consist of points in time and space at which a given…
Quadratic hedging of option payoffs generates the variance optimal martingale measure. When an option features an exercise policy and its cash flows are hedged according to this approach, it may be tempting to optimize such a policy under this measure. Because the variance optimal martingale measure may not be an equiv…
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.
Pen-and-paper exercises cover various machine learning topics.
problem None explicitly stated, focuses on learning through exercises.
method Pen-and-paper exercises on machine learning topics.
result Comprehensive coverage of machine learning concepts through exercises.
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.
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.
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…
American options in a multi-asset market model with proportional transaction costs are studied in the case when the holder of an option is able to exercise it gradually at a so-called mixed (randomised) stopping time. The introduction of gradual exercise leads to tighter bounds on the option price when compared to the …
Pricing Bermudan swaptions with few exercise dates using analytic methods.
problem Pricing Bermudan swaptions with few exercise dates
method Analytic decomposition and backward induction under rolling forward measures
result Pricing formulas with decomposition and boundary linearity
In the standard models for optimal multiple stopping problems it is assumed that between two exercises there is always a time period of deterministic length , the so called refraction period. This prevents the optimal exercise times from bunching up together on top of the optimal stopping time for the one-exercise c…
Game (Israeli) options in a multi-asset market model with proportional transaction costs are studied in the case when the buyer is allowed to exercise the option and the seller has the right to cancel the option gradually at a mixed (or randomised) stopping time, rather than instantly at an ordinary stopping time. Allo…
The pricing, hedging, optimal exercise and optimal cancellation of game or Israeli options are considered in a multi-currency model with proportional transaction costs. Efficient constructions for optimal hedging, cancellation and exercise strategies are presented, together with numerical examples, as well as probabili…
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…
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.
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…
We analyse the optimal exercise of an executive stock option (ESO) written on a stock whose drift parameter falls to a lower value at a change point, an exponentially distributed random time independent of the Brownian motion driving the stock. Two agents, who do not trade the stock, have differing information on the c…
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.
We consider the impact of ambiguity on the optimal timing of a class of two-dimensional integral option contracts when the exercise payoff is a positively homogeneous measurable function. Hence, the considered class of exercise payoffs includes discontinuous functions as well. We identify a parameterized family of exce…
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.
Develops a method for solving optimal stopping problems with multiple exercise rights.
problem Optimal stopping with multiple exercise rights under model uncertainty.
method Pathwise duality approach based on robust martingale dual representation.
result Establishes upper and lower bounds that converge to the true solution.
Nowadays many financial derivatives, such as American or Bermudan options, are of early exercise type. Often the pricing of early exercise options gives rise to high-dimensional optimal stopping problems, since the dimension corresponds to the number of underlying assets. High-dimensional optimal stopping problems are,…
The paper presents a method for personalized exercise recommendations that improves learner skill gain.
problem Adapting to individual needs in large, diverse groups of learners in digital environments.
method Contextual Thompson Sampling to select exercises that advance learner skill.
result The method recommends exercises associated with greater skill improvement and adapts to learner differences.
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).
The mathematical problem concerning intrinsic storage optimisation is formulated and solved by means of variational analysis. The solution, though obtained in implicit form, still sheds light on many important features of the optimal exercise strategy. It is shown how the solution depends on different constraint types …
This paper analyzes optimal stopping regions for American options with Poisson exercise opportunities.
problem Analyzing the optimal stopping regions for American options with Poisson exercise opportunities.
method Computing identities related to the first Poisson arrival time to an interval and applying them to the computation of the optimal strategies.
result Explicit expressions of the stopping and continuation regions and the value function are obtained.
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.
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 …
Deep Q-Learning models optimal exercise strategies for option-type products.
problem Modeling optimal exercise strategies for option-type products.
method Reinforcement learning approach using deep neural networks to approximate the Q-function.
result Pricing the contract at inception and deriving bounds on the option price.
Regularity of the Exercise Boundary for American Put Options on Assets with Discrete Dividendsq-fin.CP
We analyze the regularity of the optimal exercise boundary for the American Put option when the underlying asset pays a discrete dividend at a known time during the lifetime of the option. The ex-dividend asset price process is assumed to follow Black-Scholes dynamics and the dividend amount is a deterministic fu…
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…
The mathematical problem of the static storage optimisation is formulated and solved by means of a variational analysis. The solution obtained in implicit form is shedding light on the most important features of the optimal exercise strategy. We show how the solution depends on different constraint types including carr…
This study proposes an exercise fatigue detection model based on real-time clinical data which includes time domain analysis, frequency domain analysis, detrended fluctuation analysis, approximate entropy, and sample entropy. Furthermore, this study proposed a feature extraction method which is combined with an analyti…
New method uses CNN to solve optimal stopping problem in financial options.
problem Solving optimal stopping problem in financial option valuation.
method Employed a data-driven approach using CNN to train and test ANN for decision making.
result Our method improves accuracy in capturing optimal exercise opportunities.
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…
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.
Optimal Multiple Stopping with Negative Discount Rate and Random Refraction Times under Levy Modelsq-fin.MF
This paper studies a class of optimal multiple stopping problems driven by Lévy processes. Our model allows for a negative effective discount rate, which arises in a number of financial applications, including stock loans and real options, where the strike price can potentially grow at a higher rate than the original d…
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 propose a discrete time algorithm for the valuation of employee stock options based on exponential indifference prices and taking into account both the possibility of partial exercise of a fraction of the options and the use of a correlated traded asset to hedge part of their risk. We determine the optimal exercise …
XVA at the Exercise Boundaryq-fin.PR
XVA is a material component of a trade valuation and hence it must impact the decision to exercise options within a given netting set. This is true for both unsecured trades and secured / cleared trades where KVA and MVA play a material role even if CVA and FVA do not. However, this effect has frequently been ignored i…
The paper tracks patient recovery using graphs of joint movement data.
problem Tracking individual patient recovery trajectories in physical therapy.
method Bayesian learning of Random Geometric Graphs from joint movement data.
result Optimal exercise routines can be recommended based on patient recovery data.
We justify and give error estimates for binomial approximations of game (Israeli) options in the Black--Scholes market with Lipschitz continuous path dependent payoffs which are new also for usual American style options. We show also that rational (optimal) exercise times and hedging self-financing portfolios of binomi…
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…
Timing in the Presence of Directional Predictability: Optimal Stopping of Skew Brownian Motionmath.PR
We investigate a class of optimal stopping problems arising in, for example, studies considering the timing of an irreversible investment when the underlying follows a skew Brownian motion. Our results indicate that the local directional predictability modeled by the presence of a skew point for the underlying has a no…
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…
Explicit RKF-Compact Scheme for Pricing Regime Switching American Options with Varying Time Stepq-fin.CP
New method solves complex financial option pricing with varying time steps.
problem Pricing American options with varying time steps and regime switching.
method Explicit Runge-Kutta-Fehlberg scheme with fourth-order compact finite difference in space and high order analytical approximation.
result The method provides better performance in terms of computational speed and accuracy.
This paper studies the market phenomenon of non-convergence between futures and spot prices in the grains market. We postulate that the positive basis observed at maturity stems from the futures holder's timing options to exercise the shipping certificate delivery item and subsequently liquidate the physical grain. In …
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…