The Libor market model is a mainstay term structure model of interest rates for derivatives pricing, especially for Bermudan swaptions, and other exotic Libor callable derivatives. For numerical implementation the pricing of derivatives with Libor market models is mainly carried out with Monte Carlo simulation. The PDE…
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48 results for “Bermudan solvers”
Continuous-time optimal stopping solved with deep reinforcement learning
problem Optimal stopping problems in continuous time
method CARLOS (Continuous-time Adaptive Reinforcement Learning for Optimal Stopping)
result Higher prices than existing Bermudan solvers, approaching American upper bound
Berms without Calibrationq-fin.PR
A new model prices Bermudan swaptions without calibration.
problem Calibration of Bermudan swaptions models.
method Semi-analytical pricing model using swap rates and correlations.
result No product-specific calibration required.
Study Nash equilibrium in non-zero-sum game with Bermudan strategies.
problem Optimizing pay-offs in non-linear non-zero-sum games.
method Recursive construction to find Nash equilibrium.
result Existence of Nash equilibrium in non-zero-sum game.
Learning Bermudansq-fin.PR
New SL algorithms improve Bermudan Swaption pricing efficiency.
problem Efficient pricing of Bermudan Swaptions using Monte Carlo methods.
method Supervised Learning algorithms linking Bermudan Swaption to European Swaptions and other financial quantities.
result SL algorithms (Ridge, ANN, Gradient Boosted Regression Tree) are reliable and fast, overcoming Monte Carlo computational bottleneck.
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.
New dual approach for hedging Bermudan options efficiently.
problem Computing efficient hedging portfolios for Bermudan options.
method Pure dual approach, rewriting dual pricing formula as excess reward representation, strict convexification, Monte Carlo method.
result Convergence and effectiveness of the new algorithm tested on various Bermudan options.
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.
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.
Efficiently values and computes sensitivities of Bermudan options using Method of Lines.
problem Valuation and sensitivities of Bermudan options.
method Method of Lines converting Black Scholes PDE to ODEs, spatial discretization, exponential matrix operation for efficiency.
result Computational efficiency and straightforward implementation for computing sensitivities.
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
Efficiently price high-dimensional Bermudan options using tensor compression.
problem High-dimensional option pricing with computational complexity.
method Hierarchical tensor compression for Monte Carlo and dual martingale methods.
result Tensor compression alleviates the curse of dimensionality for Bermudan option pricing.
Paper presents a fast algorithm for pricing Bermudan swaptions under the two-factor Hull-White model.
problem Evaluating Bermudan swaption prices under the two-factor Hull-White model with high computational efficiency.
method Discretization of expected value calculation, Gaussian kernel sums, fast Gauss transform, grid rotation for stability.
result Significant reduction in computation time and improved stability for correlation close to -1.
This paper proposes two numerical solution based on Product Optimal Quantization for the pricing of Foreign Echange (FX) linked long term Bermudan options e.g. Bermudan Power Reverse Dual Currency options, where we take into account stochastic domestic and foreign interest rates on top of stochastic FX rate, hence we c…
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.
Paper optimizes neural networks for Bermudan option pricing with faster convergence and risk management tools.
problem Efficiently pricing Bermudan options with static hedging and risk management.
method Monte-Carlo-based artificial neural network framework with novel optimisation algorithm.
result The proposed neural network accelerates convergence and provides improved risk management tools.
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.
Tensor Neural Networks improve pricing accuracy for interest rate derivatives.
problem Inaccurate pricing of Bermudan Swaptions using traditional methods.
method Leveraging Tensor Neural Networks to solve backward Stochastic Differential Equations.
result Tensor Neural Networks provide more accurate and robust prices than Dense Neural Networks.
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.
Fast Calculation of Credit Exposures for Barrier and Bermudan options using Chebyshev interpolationq-fin.CP
We introduce a new method to calculate the credit exposure of Bermudan, discretely monitored barrier and European options. Core of the approach is the application of the dynamic Chebyshev method of Glau et al. (2019). The dynamic Chebyshev method delivers a closed form approximation of the option prices along the paths…
A deep learning approach for computations of exposure profiles for high-dimensional Bermudan optionsq-fin.CP
Deep learning approximates Bermudan option exposures and future values.
problem Computing accurate expected and future exposures for high-dimensional Bermudan options.
method Neural network-based approach combining Deep Optimal Stopping and regression.
result Neural network approximations of pathwise option values are more accurate.
Valuation of Credit Valuation Adjustment (CVA) has become an important field as its calculation is required in Basel III, issued in 2010, in the wake of the credit crisis. Exposure, which is defined as the potential future loss of a default event without any recovery, is one of the key elementsfor pricing CVA. This pap…
We study a Markov-Functional (MF) interest-rate model with Uncertain Volatility Displaced Diffusion (UVDD) digital mapping, which is consistent with the volatility-smile phenomenon observed in the option market. We first check the impact of pricing Bermudan swaptions by the model. Next, we also investigate the future s…
The pricing and hedging of a general class of options (including American, Bermudan and European options) on multiple assets are studied in the context of currency markets where trading is subject to proportional transaction costs, and where the existence of a risk-free numéraire is not assumed. Constructions leading t…
The problem of pricing Bermudan options using Monte Carlo and a nonparametric regression is considered. We derive optimal non-asymptotic bounds for a lower biased estimate based on the suboptimal stopping rule constructed using some estimates of continuation values. These estimates may be of different nature, they may …
The paper uses regression trees/random forests to price Bermudan options more efficiently.
problem Pricing Bermudan options with conditional expectation estimation.
method Estimates conditional expectations using regression trees or random forests instead of traditional regression methods.
result Regression trees/random forests provide better results in high dimensions.
The pricing of Bermudan options amounts to solving a dynamic programming principle, in which the main difficulty, especially in high dimension, comes from the conditional expectation involved in the computation of the continuation value. These conditional expectations are classically computed by regression techniques o…
The least squares Monte Carlo (LSM) algorithm proposed by Longstaff and Schwartz (2001) is widely used for pricing Bermudan options. The LSM estimator contains undesirable look-ahead bias, and the conventional technique of avoiding it requires additional simulation paths. We present the leave-one-out LSM (LOOLSM) algor…
We develop a mixed least squares Monte Carlo-partial differential equation (LSMC-PDE) method for pricing Bermudan style options on assets whose volatility is stochastic. The algorithm is formulated for an arbitrary number of assets and volatility processes and we prove the algorithm converges almost surely for a class …
The paper finds upper bounds for Bermudan options with convex payoffs.
problem Finding robust bounds for Bermudan options with convex payoffs.
method Characterizing and simplifying the dual problem, solving under structural assumptions on measures.
result Additional randomisation is required for optimal model definition even when marginal laws are atom-free.
A semi-static replication approach to efficient hedging and pricing of callable IR derivativesq-fin.CP
A semi-static approach efficiently replicates and prices callable interest rate derivatives.
problem Efficiently replicating and pricing callable interest rate derivatives under dynamic market conditions.
method Proposes a semi-static hedging algorithm that updates the replication portfolio on a finite number of instances, rather than continuously.
result The hedging error can be made arbitrarily small with a sufficiently large replication portfolio, and closed-form error margins are determined.
We consider a defaultable asset whose risk-neutral pricing dynamics are described by an exponential Lévy-type martingale. This class of models allows for a local volatility, local default intensity and a locally dependent Lévy measure. We present a pricing method for Bermudan options based on an analytical approximatio…
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,…
Deep BSDE method for pricing and hedging complex financial portfolios.
problem Simultaneous pricing and delta-gamma hedging of large portfolios of multi-asset Bermudan options.
method Discretely reflected BSDEs, One Step Malliavin scheme, neural network regression Monte Carlo method.
result Efficient and accurate pricing and hedging strategies for high-dimensional portfolios.
Bermudan options by simulationq-fin.CP
The aim of this study is to devise numerical methods for dealing with very high-dimensional Bermudan-style derivatives. For such problems, we quickly see that we can at best hope for price bounds, and we can only use a simulation approach. We use the approach of Barraquand & Martineau which proposes that the reward pro…
In this work, we propose a new policy iteration algorithm for pricing Bermudan options when the payoff process cannot be written as a function of a lifted Markov process. Our approach is based on a modification of the well-known Longstaff Schwartz algorithm, in which we basically replace the standard least square regre…
We investigate two new strategies for the numerical solution of optimal stopping problems within the Regression Monte Carlo (RMC) framework of Longstaff and Schwartz. First, we propose the use of stochastic kriging (Gaussian process) meta-models for fitting the continuation value. Kriging offers a flexible, nonparametr…
Optimal dual martingales, their analysis and application to new algorithms for Bermudan productsq-fin.CP
In this paper we introduce and study the concept of optimal and surely optimal dual martingales in the context of dual valuation of Bermudan options, and outline the development of new algorithms in this context. We provide a characterization theorem, a theorem which gives conditions for a martingale to be surely optim…
Fast pricing of American-style options has been a difficult problem since it was first introduced to financial markets in 1970s, especially when the underlying stocks' prices follow some jump-diffusion processes. In this paper, we propose a new algorithm to generate tight upper bounds on the Bermudan option price witho…
In this paper we consider three types of embedded options in pension benefit design. The first is the Florida second election (FSE) option, offered to public employees in the state of Florida in 2002. Employees were given the option to convert from a defined contribution (DC) plan to a defined benefit (DB) plan at a ti…
Improved Least-Squares Monte Carlo with finite-difference ansatz.
problem Improving accuracy and stability in option pricing.
method Constructing an ansatz using finite-difference solution for conditional expected continuation payoffs.
result Reduces mean squared error and final pricing error.
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.
Exact solver speeds up Weston-Watkins SVM subproblem significantly.
problem Improving performance of Weston-Watkins multiclass SVM.
method Novel reparametrization for exact subproblem solving.
result Significant speed-up over state-of-the-art solvers for large number of classes.
Optimizes neural networks with blackbox solvers using Time-cost Regularization.
problem Improving neural network performance by integrating efficient solvers for complex problems.
method Optimizes both the primary loss function and the performance of the blackbox solver using Time-cost Regularization. Introduces a hyper-blackbox concept to learn blackbox parameters.
result Significant improvement in neural network performance through optimization of blackbox solvers.
Efficient method for pricing Bermudan moving average options using GPR-GHQ.
problem High-dimensional pricing of Bermudan moving average options in energy markets.
method Gaussian Process Regression and Gauss-Hermite quadrature.
result GPR-GHQ method efficiently handles long windows and high dimensionality.
In this article, we apply the forward variance modeling approach by L.Bergomi to the co-terminal swap market model. We build an interest rate model for which all the market price changes of hedging instruments, interest rate swaps and European swaptions, are interpreted as the state variable variations, and no diffusio…
Picking Efficient Portfolios from 3,171 US Common Stocks with New Quantum and Classical Solversquant-ph
Study analyzes 3,171 stocks to pick efficient portfolios using quantum and classical solvers.
problem Creating efficient stock portfolios from a large dataset.
method Used classical and quantum solvers to optimize portfolios of 3,171 US stocks.
result Demonstrated the effectiveness of quantum and classical solvers in portfolio optimization.
New method uses reinforcement learning to calibrate financial models.
problem Finding continuous-time diffusion models that fit market option prices.
method Multi-Agent Reinforcement Learning (MARL) to search stochastic process space.
result Algorithm learns local volatility and path-dependence for Bermudan options.