New method reduces Monte Carlo error in option pricing and Greeks estimation.
problem Reducing Monte Carlo error in option pricing and Greeks estimation.
method Denoised Monte Carlo technique for LSV models.
result Reduces Monte Carlo error by an order of magnitude.
Pricing options is an important problem in financial engineering. In many scenarios of practical interest, financial option prices associated to an underlying asset reduces to computing an expectation w.r.t.~a diffusion process. In general, these expectations cannot be calculated analytically, and one way to approximat…
This study compares MC and QMC methods for derivative pricing, showing QMC's superior convergence rates.
problem Improving derivative pricing accuracy and efficiency in high-dimensional settings.
method Compared Monte Carlo and quasi-Monte Carlo techniques, focusing on convergence rates and low-discrepancy sequences.
result Quasi-Monte Carlo methods achieve superior convergence rates and reduce root mean square error in derivative pricing.
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.
Weighted Monte Carlo prices exotic options calibrating the probabilities of previously generated paths by a regular Monte Carlo to fit a set of option premiums. When only vanilla call and put options and forward prices are considered, the Martingale condition might not be preserved. This paper shows that this is indeed…
Sequential Monte Carlo (SMC) methods have successfully been used in many applications in engineering, statistics and physics. However, these are seldom used in financial option pricing literature and practice. This paper presents SMC method for pricing barrier options with continuous and discrete monitoring of the barr…
Adapts Monte Carlo method to price π-options related to maximum drawdown.
problem Pricing π-options in volatile market conditions.
method Monte Carlo algorithm with simulated price tree.
result Algorithm produces bounds converging to true price with tree depth.
A fast Monte Carlo method for additive processes and option pricing.
problem Efficiently pricing path-dependent options with additive processes.
method Developed a fast Monte Carlo scheme for additive processes, analyzing and reducing numerical error sources.
result Shows significant reduction in error (1 bp or below) for pricing path-dependent options.
Quantum Monte Carlo speeds up option pricing for complex payoff functions.
problem Efficiently pricing options with complex payoff functions using quantum computing.
method Developed a quantum Monte Carlo algorithm for multidimensional Black-Scholes PDEs.
result Proved polynomial computational complexity and speed-up over classical methods.
We introduce a stacking version of the Monte Carlo algorithm in the context of option pricing. Introduced recently for aeronautic computations, this simple technique, in the spirit of current machine learning ideas, learns control variates by approximating Monte Carlo draws with some specified function. We describe the…
A new two-step LSMC method improves game option pricing accuracy.
problem Improving game option pricing accuracy using Monte Carlo methods.
method Proposed a two-step Longstaff Schwartz Monte Carlo approach with two regression models fitted at each time step.
result Our method produces more reliable results compared to the original LSMC.
Quantum computing improves Monte Carlo option pricing for complex derivatives.
problem Complex financial derivatives require extensive computations in high-dimensional spaces.
method Developed a quantum algorithm for simulating many potential asset paths in parallel.
result Quantum algorithm provides highly accurate option pricing and risk analysis.
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.
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.
One of the main practical applications of quasi-Monte Carlo (QMC) methods is the valuation of financial derivatives. We aim to give a short introduction into option pricing and show how it is facilitated using QMC. We give some practical examples for illustration.
Study compares MC and QMC methods for pricing and risk analysis in a hyperbolic local volatility model.
problem Derivative pricing and risk analysis in a hyperbolic local volatility model.
method Application of Monte Carlo and Quasi Monte Carlo methods for pricing and risk analysis.
result Quasi Monte Carlo methods show superior performance in high-dimensional integration for derivative pricing and risk analysis.
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.
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.
New method for pricing discrete Asian and Lookback options under Heston model.
problem Efficient pricing of discrete Asian and Lookback options under Heston model.
method Data-driven approach using artificial neural networks and stochastic collocation points.
result High accuracy and significant computational time reduction compared to classical methods.
Efficient hybrid method for pricing barrier options with stochastic volatility.
problem Valuation of barrier options on assets with stochastic volatility.
method Combining Monte Carlo simulation and semi-analytical heat potential method.
result Our method provides better accuracy and is orders of magnitude faster than existing methods.
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.
The use of sequential Monte Carlo within simulation for path-dependent option pricing is proposed and evaluated. Recently, it was shown that explicit solutions and importance sampling are valuable for efficient simulation of spot price and volatility, especially for purposes of path-dependent option pricing. The result…
A hybrid framework prices options using neural networks and VAE latent space.
problem Lack of explicit asset dynamics information in compressed volatility surfaces.
method Combining Weighted Monte Carlo with neural networks trained on VAE latent space.
result Effective pricing of vanilla and exotic options on idealized vol surface.
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…
Option valuation problems are often solved using standard Monte Carlo (MC) methods. These techniques can often be enhanced using several strategies especially when one discretizes the dynamics of the underlying asset, of which we assume follows a diffusion process. We consider the combination of two methodologies in th…
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.
This research improves option pricing models using Heston, GARCH, and jump diffusion models.
problem Inaccurate option pricing due to Black-Scholes assumptions.
method Monte Carlo simulation, GARCH model, Heston model, Merton jump-diffusion model.
result Heston model produces estimates closer to market prices, Merton model performs well for volatile assets, GARCH model improves volatility forecasts.
The thesis examines stochastic calculus in option pricing with logistic models and numerical methods.
problem Exploring the application of stochastic calculus in option pricing.
method Monte-Carlo Simulation and machine learning algorithms.
result Insights from Peter Carr and Lorenzo Torricelli's convex duality in continuous models.
Barrier options are one of the most widely traded exotic options on stock exchanges. In this paper, we develop a new stochastic simulation method for pricing barrier options and estimating the corresponding execution probabilities. We show that the proposed method always outperforms the standard Monte Carlo approach an…
Efficiently price VIX options using multilevel Monte Carlo in rough Bergomi model.
problem Pricing VIX options in a rough Bergomi model with high computational complexity.
method Combining rectangle discretization, Cholesky sampling, and multilevel Monte Carlo.
result Reduced computational complexity to O(ε−2log2(ε)) and asymptotically optimal O(ε−2). This paper uses Monte Carlo simulation to value quality options in agricultural futures contracts.
problem Valuation of quality options in agricultural futures to prevent manipulation and improve hedging performance.
method Monte Carlo simulation with antithetic variables for efficiency.
result Demonstrates a method to estimate the value of quality options in agricultural futures contracts.
A new method predicts future paths using a Monte-Carlo approach.
problem Predicting future financial paths given historical data.
method Path Shadowing Monte-Carlo method using maximum entropy model.
result Yields state-of-the-art predictions for future volatility and option smiles.
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.
High performance computing (HPC) is a very attractive and relatively new area of research, which gives promising results in many applications. In this paper HPC is used for pricing of American options. Although the American options are very significant in computational finance; their valuation is very challenging, espe…
Deep learning improves option pricing for a non-martingale asset model.
problem Computing call option prices for the Barndorff-Nielsen and Shephard model with infinite jumps.
method Developed a supervised deep-learning scheme using Monte Carlo teaching data and a Black-Scholes-derived variable.
result Significant improvement in accuracy of option pricing.
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 proposes a closed-form formula for geometric Istanbul call options.
problem Pricing geometric Istanbul call options under the Black-Scholes model.
method Second-order Taylor expansion to derive a closed-form approximation.
result The proposed formula accurately approximates GIC values compared to Monte-Carlo simulations.
Quantum methods improve option pricing accuracy.
problem Pricing financial derivatives using Monte Carlo integration.
method Hybrid classical-quantum methods using Fourier series and QML.
result Quantum methods achieve remarkable accuracy in option pricing.
The pricing of financial derivatives, which requires massive calculations and close-to-real-time operations under many trading and arbitrage scenarios, were largely infeasible in the past. However, with the advancement of modern computing, the efficiency has substantially improved. In this work, we propose and design a…
In this paper, we discuss the application of quasi-Monte Carlo methods to the Heston model. We base our algorithms on the Broadie-Kaya algorithm, an exact simulation scheme for the Heston model. As the joint transition densities are not available in closed-form, the Linear Transformation method due to Imai and Tan, a p…
Fast, reliable, and error-bounded option pricing with neural networks
problem Fast, reliable, and error-bounded option pricing
method Mixture Density Network
result Out-of-sample CDF error of 1.4imes10−4 Quantum computing speeds up option pricing for multiple assets.
problem High-dimensional integration bottleneck in option pricing.
method Calibrated marginal distributions, Gaussian copula, QAMC with QAE.
result QAMC reduces integration queries by 10-100 times for similar precision.
QMC and GSA improve option pricing and risk measures efficiency.
problem Efficiently pricing and hedging complex financial instruments.
method Application of QMC and GSA techniques for financial instrument pricing and hedging, comparing MC vs QMC and analyzing greeks computation.
result QMC outperforms MC in most cases, especially in high-dimensional simulations, leading to faster and more stable convergence.
ANN improves option pricing models by calibrating parameters faster and more accurately.
problem Calibration of GARCH-type option pricing models is computationally intensive and model-dependent.
method Trained ANN models on Monte Carlo simulation data to calibrate GARCH parameters.
result ANN outperforms traditional methods in calibration speed and accuracy.
We describe general multilevel Monte Carlo methods that estimate the price of an Asian option monitored at m fixed dates. Our approach yields unbiased estimators with standard deviation O(ε) in O(m+(1/ε)2) expected time for a variety of processes including the Black-Scholes model, Merton's jump-diffusion mod…
In this paper, a standard PDE for the pricing of arithmetic average strike Asian call option is presented. A Crank-Nicolson Implicit Method and a Higher Order Compact finite difference scheme for this pricing problem is derived. Both these schemes were implemented for various values of risk free rate and volatility. Th…
Develops numerical methods for pricing exchange options in a market with limited liquidity.
problem Pricing European style exchange options in a market with finite liquidity.
method Integrates price impact into the dynamics of correlated assets using a controlled variate approach.
result Numerical pricing methods for exchange options are developed and validated.
Typically options with a path dependent payoff, such as Target Accumulation Redemption Note (TARN), are evaluated by a Monte Carlo method. This paper describes a finite difference scheme for pricing a TARN option. Key steps in the proposed scheme involve tracking of multiple one-dimensional finite difference solutions,…