Speeds up complex portfolio exposure calculations.
problem Calculating exposure of portfolios with exotic derivatives.
method Least Squares Monte Carlo (LSMC) technique.
result Significantly reduces computation time for nested Monte Carlo.
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48 results for “least squares Monte Carlo”
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.
Developed scalable Monte Carlo method for VIX option pricing.
problem VIX option pricing in stochastic Volterra rough volatility models with non-Markovian vol-of-vol.
method Infinite dimensional Markovian representation to devise scalable least squares Monte Carlo.
result Efficient VIX option pricing method for generalized models.
The paper uses LSMC to price capped American options with time-dependent caps.
problem Pricing American options with time-capped features.
method Least Squares Monte Carlo (LSMC) method.
result The LSMC method converges to the true price as discretization step and number of trajectories approach limits.
Consider Least Squares Monte Carlo (LSM) algorithm, which is proposed by Longstaff and Schwartz (2001) for pricing American style securities. This algorithm is based on the projection of the value of continuation onto a certain set of basis functions via the least squares problem. We analyze the stability of the algori…
This paper explores alternative regression techniques in pricing American put options and compares to the least-squares method (LSM) in Monte Carlo implemented by Longstaff-Schwartz, 2001 which uses least squares to estimate the conditional expected payoff to the option holder from continuation. The pricing is done und…
A recently introduced Importance Sampling strategy based on a least squares optimization is applied to the Monte Carlo simulation of Libor Market Models. Such Least Squares Importance Sampling (LSIS) allows the automatic optimization of the sampling distribution within a trial class by means of a quick presimulation al…
The paper uses LSM to solve complex monetary utility functions.
problem Computing dynamic monetary utility functions with high dimensions.
method Least Squares Monte Carlo (LSM) algorithm.
result LSM algorithm successfully applied to recursive Cost-of-Capital valuation.
How many inner simulations to compute conditional expectations with least-square Monte Carlo?math.ST
Optimizes K inner simulations for least-square Monte Carlo to reduce computational cost.
problem Computing conditional expectation E[f (Y)|X] with limited samples.
method Determines optimal number of Y samples (K) for given computational budget.
result Computational gain is maximized when sampling Y given X is inexpensive.
Quantum algorithm speeds up financial option pricing.
problem Optimizing stopping times in stochastic processes for finance.
method Combines quantum computing techniques with LSM for optimal stopping.
result Achieves nearly quadratic speedup in runtime.
Derivatives on the Chicago Board Options Exchange volatility index (VIX) have gained significant popularity over the last decade. The pricing of VIX derivatives involves evaluating the square root of the expected realised variance which cannot be computed by direct Monte Carlo methods. Least squares Monte Carlo methods…
We describe a simple Importance Sampling strategy for Monte Carlo simulations based on a least squares optimization procedure. With several numerical examples, we show that such Least Squares Importance Sampling (LSIS) provides efficiency gains comparable to the state of the art techniques, when the latter are known to…
Efficient method for high-dimensional American option pricing and hedging.
problem High-dimensional American option pricing and hedging.
method Gradient-enhanced sparse Hermite polynomial expansions combined with least squares Monte Carlo.
result Outperforms state-of-the-art methods in high dimensions with comparable computational cost.
Local Control Regression: Improving the Least Squares Monte Carlo Method for Portfolio Optimizationq-fin.PM
The least squares Monte Carlo algorithm has become popular for solving portfolio optimization problems. A simple approach is to approximate the value functions on a discrete grid of portfolio weights, then use control regression to generalize the discrete estimates. However, the classical global control regression can …
Many problems in financial engineering involve the estimation of unknown conditional expectations across a time interval. Often Least Squares Monte Carlo techniques are used for the estimation. One method that can be combined with Least Squares Monte Carlo is the "Regress-Later" method. Unlike conventional methods wher…
Improves accuracy of SMCI estimators without expanding sum regions.
problem Intractable multiple summations in evaluating expectations on the Ising model.
method Combining multiple SMCI estimators using generalized least squares (GLS).
result The proposed method can improve accuracy without combinatorial explosion.
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…
The pricing of American style and multiple exercise options is a very challenging problem in mathematical finance. One usually employs a Least-Square Monte Carlo approach (Longstaff-Schwartz method) for the evaluation of conditional expectations which arise in the Backward Dynamic Programming principle for such optimal…
New algorithm reduces bias and variance in weighted least-squares solutions.
problem Inconsistent linear least-squares problems with rapidly decaying singular values.
method Regularized block Kaczmarz (ReBlocK) algorithm.
result ReBlocK outperforms RBK and minibatch SGD for inconsistent problems.
Reinforced optimal controlmath.OC
Improved reinforcement method for optimal control problems.
problem Optimal control problems with limited computational cost.
method Reinforced least squares Monte Carlo method for stochastic control problems.
result Significant improvement in method's efficiency and accuracy.
This article presents a stochastic framework to quantify the biometric risk of an insurance portfolio in solvency regimes such as Solvency II or the Swiss Solvency Test (SST). The main difficulty in this context constitutes in the proper representation of long term risks in the profit-loss distribution over a one year …
A Monte Carlo k-nearest neighbours (KNN) and a multi-resolution convolutional neural network (CNN) were developed to detect the presences of multiple gasses in near infrared (IR) spectrums. High Resolution Transmission database was used to synthesize the near IR spectrums. Monte Carlo KNN determined the optimal kernel …
Machine learning improves American option pricing accuracy.
problem Complexities of American options and traditional models' limitations.
method Monte Carlo simulations combined with machine learning algorithms (Least Square Method, LSTM, GRU).
result GRU model outperforms LSTM in predicting bid prices, enhancing accuracy and stability.
Under the Solvency II regime, life insurance companies are asked to derive their solvency capital requirements from the full loss distributions over the coming year. Since the industry is currently far from being endowed with sufficient computational capacities to fully simulate these distributions, the insurers have t…
New method for unbiased regression reduces excess risk.
problem Least squares regression with optimal solution and Hessian matrix.
method Averaged stochastic gradient descent with time-average estimator.
result Unbiased estimator with O(1/k) expected excess risk.
We propose a new forward-backward stochastic differential equation solver for high-dimensional derivatives pricing problems by combining deep learning solver with least square regression technique widely used in the least square Monte Carlo method for the valuation of American options. Our numerical experiments demonst…
We propose a methodology for computing single and multi-asset European option prices, and more generally expectations of scalar functions of (multivariate) random variables. This new approach combines the ability of Monte Carlo simulation to handle high-dimensional problems with the efficiency of function approximation…
Pricing commodity swing optionsq-fin.PR
The paper models natural gas futures prices and volatility, using Monte Carlo and reinforcement learning.
problem Hedging and selecting delivery strategies in natural gas markets.
method Dynamical model for futures prices, least-square Monte Carlo simulation, reinforcement learning.
result Calibrated futures price quotes and implied volatility smiles for different delivery periods.
Paper improves ISDA margin calculation using LSMC.
problem Efficiently calculating initial margin for financial contracts.
method Extends Least Squares Monte-Carlo (LSMC) technique.
result Improved efficiency in estimating margin sensitivities.
Bayesian method improves parameter reconstruction from many measurements.
problem Efficiently reconstructing parameters from many experimental measurements.
method Bayesian target-vector optimization considering all model outputs.
result Outperforms established optimization methods in accuracy and efficiency.
Paper proposes method for generating paths of stochastic volatility CGMY process for option pricing.
problem Generating accurate sample paths for stochastic volatility models for option pricing.
method Monte-Carlo method for European and American options, least square regression for calibration.
result Calibrated model parameters to S\&P 100 index options market using path-dependent options.
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.
We introduce a new method to price American-style options on underlying investments governed by stochastic volatility (SV) models. The method does not require the volatility process to be observed. Instead, it exploits the fact that the optimal decision functions in the corresponding dynamic programming problem can be …
A machine learning approach to portfolio pricing and risk management for high-dimensional problemsq-fin.RM
A machine learning model manages portfolio risk in high dimensions.
problem Managing risk in high-dimensional financial portfolios.
method A supervised learning approach using replicating martingales and polynomial/neural network bases.
result The model outperforms naive Monte Carlo and least-squares Monte Carlo methods.
The paper proposes efficient methods to learn VaR and ES using neural networks and Monte Carlo simulations.
problem Learning conditional VaR and ES in non-parametric setups with heavy-tailed financial losses.
method Two-step approach using Rademacher bounds, neural network quantile regression, and least-squares regression.
result Efficient learning schemes for multiple VaRs and ES are developed.
New PCA method for derivatives problems.
problem Reducing dimensionality in derivatives pricing models.
method Supervised Principal Component Analysis (PCA)
result Improved accuracy in machine learning applications.
Within the Own Risk and Solvency Assessment framework, the Solvency II directive introduces the need for insurance undertakings to have efficient tools enabling the companies to assess the continuous compliance with regulatory solvency requirements. Because of the great operational complexity resulting from each comple…
Parallel American Monte Carloq-fin.CP
In this paper we introduce a new algorithm for American Monte Carlo that can be used either for American-style options, callable structured products or for computing counterparty credit risk (e.g. CVA or PFE computation). Leveraging least squares regressions, the main novel feature of our algorithm is that it can be fu…
KANOP uses KANs to efficiently price American options.
problem Efficiently pricing American options with limited data.
method Combines KANs with LSMC to estimate continuation value.
result KANOP provides more accurate option value estimates.
Multilevel Monte-Carlo for computing the SCR with the standard formula and other stress testsq-fin.CP
Paper uses MLMC for SCR calculation and stress tests, showing computational efficiency.
problem Computing SCR and stress tests for insurance companies.
method Multilevel Monte-Carlo (MLMC) estimator for maximum of conditional expectations.
result MLMC estimator is computationally more efficient and avoids regression issues.
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.
In this paper, we propose a novel investment strategy for portfolio optimization problems. The proposed strategy maximizes the expected portfolio value bounded within a targeted range, composed of a conservative lower target representing a need for capital protection and a desired upper target representing an investmen…
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…
The paper provides mean-square error bounds for stochastic approximation algorithms.
problem Error bounds for recursive equations with Markovian disturbances.
method Analysis of mean-square error for stochastic approximation algorithms.
result Mean-square error achieves the optimal rate of under certain conditions.
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.
A new explicit scheme calculates XVA adjustments using neural networks and conditional expectations.
problem Calculating cross valuation adjustments (XVA) in realistic financial scenarios.
method Simulation/regression scheme for BSDEs, using neural networks and quantile regressions.
result The scheme outperforms Picard iterations in high-dimensional and hybrid market risks.
Deep Least Squares Monte Carlo methods for the valuation of variable annuities with guaranteesq-fin.PR
Paper presents deep LSMC method for efficient variable annuity pricing.
problem Efficiently pricing variable annuities with guarantees using simulation methods.
method Modifies least-squares Monte Carlo (LSMC) algorithm for optimal stochastic control problems.
result Deep LSMC provides more stable and robust pricing performance for higher-dimensional problems.
Hess-MC2: Sequential Monte Carlo Squared using Hessian Information and Second Order Proposalsstat.ML
Enhances SMC² with Hessian info for more efficient posterior approximation.
problem Improving accuracy and efficiency in Bayesian inference.
method Integrates second-order information (Hessian) into SMC²'s proposal distribution.
result Second-order proposals lead to more accurate posterior approximations and better step-size selection.