scholarly journals Pricing the exotic: Path-dependent American options with stochastic barriers

2021 ◽  
Author(s):  
Alejandro Rojas-Bernal ◽  
Mauricio Villamizar-Villegas
Keyword(s):  
Risk Factors ◽  
Monte Carlo ◽  
Analytical Solution ◽  
American Options ◽  
Pricing Strategy ◽  
Computational Time ◽  
European Options ◽  
Standard Methods ◽  
Path Dependent ◽  
Closed Form Approximation

We develop a novel pricing strategy that approximates the value of an American option with exotic features through a portfolio of European options with different maturities. Among our findings, we show that: (i) our model is numerically robust in pricing plain vanilla American options; (ii) the model matches observed bids and premiums of multidimensional options that integrate Ratchet, Asian, and Barrier characteristics; and (iii) our closed-form approximation allows for an analytical solution of the option’s greeks, which characterize the sensitivity to various risk factors. Finally, we highlight that our estimation requires less than 1% of the computational time compared to other standard methods, such as Monte Carlo simulations.

Pricing of path-dependent American options by Monte Carlo simulation

2007 ◽  
Vol 31 (11) ◽  
pp. 3478-3502 ◽  
Author(s):  
Hajime Fujiwara ◽  
Masaaki Kijima
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
American Options ◽  
Path Dependent

LOCALIZED MONTE CARLO ALGORITHM TO COMPUTE PRICES OF PATH DEPENDENT OPTIONS ON TREES

2005 ◽  
Vol 08 (05) ◽  
pp. 553-574 ◽  
Author(s):  
SEBASTIAN E. FERRANDO ◽  
ARIEL J. BERNAL
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Algorithm ◽  
European Options ◽  
General Applicability ◽  
Underlying Process ◽  
Monte Carlo Algorithms ◽  
Simulation Based ◽  
Path Dependent ◽  
Probabilistic Error

A new simulation based algorithm to approximate prices of path dependent European options is introduced. The algorithm is defined for tree-like approximations to the underlying process and makes extensive use of structural properties of the discrete approximation. We indicate the advantages of the new algorithm in comparison to standard Monte Carlo algorithms. In particular, we prove a probabilistic error bound that compares the quality of both approximations. The algorithm is of general applicability and, for a large class of options, it has the same computational complexity as Monte Carlo.

scholarly journals A Comparative Analysis of Monte Carlo and Quasi-Monte Carlo Methods in Financial Derivative Pricing

2021 ◽  
Vol 69 (1) ◽  
pp. 1-6
Author(s):  
SM Arif Hossen ◽  
ABM Shahadat Hossain
Keyword(s):  
Monte Carlo ◽  
Comparative Analysis ◽  
Monte Carlo Methods ◽  
American Options ◽  
Financial Derivatives ◽  
Numerical Results ◽  
Derivative Pricing ◽  
Quasi Monte Carlo ◽  
Financial Derivative ◽  
Path Dependent

The main purpose of this dissertation is to study Monte Carlo (MC) and Quasi-Monte Carlo (QMC) methods for pricing financial derivatives. We estimate the Price of European as well as various path dependent options like Asian, Barrier and American options by using these methods. We also compute the numerical results by the above mentioned methods and compare them graphically as well with the help of the MATLAB Coding. Dhaka Univ. J. Sci. 69(1): 1-6, 2021 (January)

Just-In-Time Monte Carlo for Path-Dependent American Options

2008 ◽  
Vol 15 (4) ◽  
pp. 29-47 ◽  
Author(s):  
Samir K. Dutt ◽  
Gerd M. Welke
Keyword(s):  
Monte Carlo ◽  
American Options ◽  
Just In Time ◽  
Path Dependent

PRICING EUROPEAN OPTIONS ON REGIME-SWITCHING ASSETS: A COMPARATIVE STUDY OF MONTE CARLO AND FINITE-DIFFERENCE APPROACHES

2017 ◽  
Vol 59 (2) ◽  
pp. 183-199 ◽  
Author(s):  
X. C. ZENG ◽  
I. GUO ◽  
S. P. ZHU
Keyword(s):  
Monte Carlo ◽  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Regime Switching ◽  
Computational Time ◽  
Switching Frequency ◽  
Numerical Comparison ◽  
European Options ◽  
Mc Simulation

A numerical comparison of the Monte Carlo (MC) simulation and the finite-difference method for pricing European options under a regime-switching framework is presented in this paper. We consider pricing options on stocks having two to four volatility regimes. Numerical results show that the MC simulation outperforms the Crank–Nicolson (CN) finite-difference method in both the low-frequency case and the high-frequency case. Even though both methods have linear growth, as the number of regimes increases, the computational time of CN grows much faster than that of MC. In addition, for the two-state case, we propose a much faster simulation algorithm whose computational time is almost independent of the switching frequency. We also investigate the performances of two variance-reduction techniques: antithetic variates and control variates, to further improve the efficiency of the simulation.

Simulation-Based Seismic Hazard Assessment Using Monte-Carlo Earthquake Catalogs: Application to CyberShake

2021 ◽  
Author(s):  
Sarah Azar ◽  
Mayssa Dabaghi
Keyword(s):  
Monte Carlo ◽  
Seismic Hazard ◽  
Ground Motion ◽  
Seismic Hazard Assessment ◽  
Computational Time ◽  
Earthquake Catalog ◽  
Earthquake Catalogs ◽  
Earthquake Scenarios ◽  
Simulation Based ◽  
Hazard Curves

ABSTRACT The use of numerical simulations in probabilistic seismic hazard analysis (PSHA) has achieved a promising level of reliability in recent years. One example is the CyberShake project, which incorporates physics-based 3D ground-motion simulations within seismic hazard calculations. Nonetheless, considerable computational time and resources are required due to the significant processing requirements imposed by source-based models on one hand, and the large number of seismic sources and possible rupture variations on the other. This article proposes to use a less computationally demanding simulation-based PSHA framework for CyberShake. The framework can accurately represent the seismic hazard at a site, by only considering a subset of all the possible earthquake scenarios, based on a Monte-Carlo simulation procedure that generates earthquake catalogs having a specified duration. In this case, ground motions need only be simulated for the scenarios selected in the earthquake catalog, and hazard calculations are limited to this subset of scenarios. To validate the method and evaluate its accuracy in the CyberShake platform, the proposed framework is applied to three sites in southern California, and hazard calculations are performed for earthquake catalogs with different lengths. The resulting hazard curves are then benchmarked against those obtained by considering the entire set of earthquake scenarios and simulations, as done in CyberShake. Both approaches yield similar estimates of the hazard curves for elastic pseudospectral accelerations and inelastic demands, with errors that depend on the length of the Monte-Carlo catalog. With 200,000 yr catalogs, the errors are consistently smaller than 5% at the 2% probability of exceedance in 50 yr hazard level, using only ∼3% of the entire set of simulations. Both approaches also produce similar disaggregation patterns. The results demonstrate the potential of the proposed approach in a simulation-based PSHA platform like CyberShake and as a ground-motion selection tool for seismic demand analyses.

scholarly journals Nesting Monte Carlo for high-dimensional non-linear PDEs

2018 ◽  
Vol 24 (4) ◽  
pp. 225-247 ◽  
Author(s):  
Xavier Warin
Keyword(s):  
Monte Carlo ◽  
Deep Learning ◽  
High Dimension ◽  
Analytical Solutions ◽  
New Method ◽  
Computational Time ◽  
High Dimensional ◽  
Learning Methods ◽  
Lipschitz Constants ◽  
Linear Pdes

Abstract A new method based on nesting Monte Carlo is developed to solve high-dimensional semi-linear PDEs. Depending on the type of non-linearity, different schemes are proposed and theoretically studied: variance error are given and it is shown that the bias of the schemes can be controlled. The limitation of the method is that the maturity or the Lipschitz constants of the non-linearity should not be too high in order to avoid an explosion of the computational time. Many numerical results are given in high dimension for cases where analytical solutions are available or where some solutions can be computed by deep-learning methods.

scholarly journals Land subsidence modelling for decision making on groundwater abstraction under emergency situation

2020 ◽  
Vol 382 ◽  
pp. 403-408
Author(s):  
Masaatsu Aichi
Keyword(s):  
Decision Making ◽  
Monte Carlo ◽  
Uncertainty Analysis ◽  
Real Time ◽  
Land Subsidence ◽  
Null Space ◽  
Emergency Situation ◽  
Computational Time ◽  
Groundwater Abstraction ◽  
Emergency Situations

Abstract. This study presents an inversion scheme with uncertainty analysis for a land subsidence modelling by a Monte Carlo filter in order to contribute to the decision-making on the groundwater abstraction. For real time prediction and uncertainty analysis under the limited computational resources and available information in emergency situations, one dimensional vertical land subsidence simulation was adopted for the forward modelling and the null-space Monte Carlo method was applied for the effective resampling. The proposed scheme was tested with the existing land subsidence monitoring data in Tokyo lowland, Japan. The results demonstrated that the prediction uncertainty converges and the prediction accuracy improves as the observed data increased with time. The computational time was also confirmed to be acceptable range for a real time execution with a laptop.

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