A new method for pricing American options using exercise rate optimization.
problem Pricing American options efficiently and accurately.
method Monte Carlo simulation and optimization of exercise rates.
result The method provides the correct option price and is efficient for various models.
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 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.
Closed-form solution found for American put option boundary.
problem Finding the optimal exercise boundary for American put options.
method Three models of stock price dynamics with time-dependent parameters, leading to a closed-form solution for the exercise boundary.
result Explicit closed-form solution for the optimal exercise boundary of American put options.
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).
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.
Machine learning predicts exercise load from heart rate data post-exercise.
problem Monitoring energy expenditure in real life.
method Machine learning methods (linear regression, etc.) applied to heart rate data.
result Random forest and k-nearest neighbors classifiers predict load levels accurately.
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…
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.
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.
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…
Optimizing option exercise policies based on variance optimal martingale measure can lead to unappealing results.
problem Optimizing American option exercise policies under the variance optimal martingale measure can result in unappealing policies.
method Optimizing option exercise policies under the variance optimal martingale measure, then anchoring to the resulting value of this policy.
result Optimizing option exercise policies based on the variance optimal martingale measure can lead to unappealing results.
Machine learning assesses balance outside clinics, improving therapy efficiency.
problem Lack of feedback from PTs in home balance training.
method Trunk sway data analysis with multi-class SVM.
result ML model achieved 82% accuracy in assessing balance.
Optimal exercise boundary for put options with delivery lags identified.
problem Analyzing the optimal exercise time for American put options with delivery lags.
method Decomposing the option into a European put and a new American-style derivative, using free boundary techniques.
result The optimal exercise boundary exists and is a strictly increasing and smooth curve.
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.
Game options study gradual exercise and cancellation with transaction costs.
problem Analyzing game options with gradual exercise and cancellation under proportional transaction costs.
method Developed algorithmic constructions for bid and ask prices, superhedging strategies, and optimal mixed stopping times.
result Increased flexibility in hedging leads to tighter bounds on option price.
Two sweeps of the Brennan-Schwartz algorithm solve American options under negative rates.
problem Inability of the Brennan-Schwartz algorithm to solve American options under negative interest rates.
method Two sweeps of the Brennan-Schwartz algorithm in two directions.
result Recovery of the exact solution for American options under negative rates.
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.
The paper explains why futures prices often differ from spot prices in grain markets.
problem Non-convergence of futures and spot prices in grains markets.
method Incorporates stochastic spot price and storage cost, solves an optimal double stopping problem.
result Explicit no-arbitrage prices for shipping certificates and futures contracts are derived.
Optimal exercise timing of stock options analyzed with varying information on drift change.
problem Analyzing optimal exercise timing of stock options with varying information on drift change.
method Rigorous mathematical analysis and numerical methods to solve optimal stopping problems.
result Characterization of optimal exercise boundaries and smooth pasting properties in both information scenarios.
Investors often miss out on early exercise of American options with dividends, volatility, and jumps.
problem Investors suboptimal exercise of American call options on dividend-paying stocks.
method Used a fast numerical technique to analyze a large database of investor decisions and incorporated stochastic volatility and jumps in pricing models.
result Pricing models with stochastic volatility and jumps reduce the loss from suboptimal exercise by a quarter.
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 q 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…
This article combines various methods of analysis to draw a comprehensive picture of penalty approximations to the value, hedge ratio, and optimal exercise strategy of American options. While convergence of the penalised solution for sufficiently smooth obstacles is well established in the literature, sharp rates of co…
We study American swaptions in the linear-rational (LR) term structure model introduced in [5]. The American swaption pricing problem boils down to an optimal stopping problem that is analytically tractable. It reduces to a free-boundary problem that we tackle by the local time-space calculus of [7]. We characterize th…
System recommends workouts and predicts success rates using RNNs.
problem Promoting healthy lifestyles through personalized exercise recommendations.
method Two interconnected recurrent neural networks (RNNs) using historical workout data.
result Interconnected-RNN model predicts exercise success rates with improved accuracy.
New method simplifies analysis of exercise timing for ambiguous integral option contracts.
problem Impact of ambiguity on optimal exercise timing of integral option contracts.
method Parameterized family of excessive functions generating supermartingales, simplifying multidimensional problem to one-dimensional static optimization.
result Value of optimal policy and worst case measure expressed in terms of these processes.
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 δ, 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…
Research examines GMIB and reset options in variable annuities.
problem Understanding the value and rationality of GMIB and reset options.
method Exploration of various parameters affecting GMIB value and calculation of critical future interest rates for reset option rationality.
result Insight into how future market performance and interest rates influence policyholder and insurer actions.
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…
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…
New pricing methods for α-quantile and early-exercise options using Spitzer identities.
problem Pricing perpetual Bermudan and American options and α-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.
Novel pricing method for equity-indexed annuities under uncertain volatility and stochastic interest rate.
problem Pricing equity-indexed annuities with early surrender risk under uncertain market conditions.
method Advanced financial modeling techniques, including uncertain volatility framework and Hull-White model for interest rate dynamics. Numerical algorithm using tree-based framework with local volatility optimization.
result High effectiveness of the proposed numerical algorithm compared to machine learning-based methods.
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.
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.
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.
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.
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.
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 …
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.
We introduce a tractable multi-currency model with stochastic volatility and correlated stochastic interest rates that takes into account the smile in the FX market and the evolution of yield curves. The pricing of vanilla options on FX rates can be performed effciently through the FFT methodology thanks to the affinit…
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 O(1/N4) and complexity of O(MNlogN). Improved fourth-order compact scheme for option valuation with Robin boundary condition.
problem Lower convergence rates in numerical methods for American options.
method High-order compact scheme, Robin boundary condition, coupled nonlinear PDEs.
result Fourth-order convergence rate achieved without mesh refinement.
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 …
Model detects exercise fatigue with high accuracy.
problem Detecting exercise fatigue in real-time.
method Feature extraction using AHP, machine learning.
result 98.65% accuracy in detecting exercise fatigue.
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.