Conservative Third-Order Central-Upwind Schemes for Option Pricing Problems

2019 ◽  
Vol 47 (4) ◽  
pp. 813-833
Author(s):  
Omishwary Bhatoo ◽  
Arshad Ahmud Iqbal Peer ◽  
Eitan Tadmor ◽  
Désiré Yannick Tangman ◽  
Aslam Aly El Faidal Saib
Keyword(s):  
Option Pricing ◽  
Third Order ◽  
Upwind Schemes ◽  
Pricing Problems

Efficient conservative second-order central-upwind schemes for option-pricing problems

2019 ◽  
Vol 22 (5) ◽  
pp. 71-101 ◽  
Author(s):  
Omishwary Bhatoo ◽  
Arshad Ahmud Iqbal Peer ◽  
Eitan Tadmor ◽  
Desire Yannick Tangman ◽  
Aslam Aly El Faidal Saib
Keyword(s):  
Option Pricing ◽  
Second Order ◽  
Upwind Schemes ◽  
Pricing Problems

scholarly journals Unconditional Positive Stable Numerical Solution of Partial Integrodifferential Option Pricing Problems

2015 ◽  
Vol 2015 ◽  
pp. 1-10
Author(s):  
M. Fakharany ◽  
R. Company ◽  
L. Jódar
Keyword(s):  
Option Pricing ◽  
Numerical Solution ◽  
Numerical Solutions ◽  
Stable Process ◽  
Integration Formula ◽  
Pricing Models ◽  
Integral Term ◽  
Pricing Problems ◽  
Stability And Consistency ◽  
Partial Integrodifferential Equation

This paper is concerned with the numerical solution of partial integrodifferential equation for option pricing models under a tempered stable process known as CGMY model. A double discretization finite difference scheme is used for the treatment of the unbounded nonlocal integral term. We also introduce in the scheme the Patankar-trick to guarantee unconditional nonnegative numerical solutions. Integration formula of open type is used in order to improve the accuracy of the approximation of the integral part. Stability and consistency are also studied. Illustrative examples are included.

scholarly journals A mixed derivative terms removing method in multi-asset option pricing problems

2016 ◽  
Vol 60 ◽  
pp. 108-114 ◽  
Author(s):  
R. Company ◽  
V.N. Egorova ◽  
L. Jódar ◽  
F. Soleymani
Keyword(s):  
Option Pricing ◽  
Mixed Derivative ◽  
Pricing Problems

Tri-Diagonal Preconditioner for Toeplitz Systems from Finance

2011 ◽  
Vol 1 (1) ◽  
pp. 82-88
Author(s):  
Hong-Kui Pang ◽  
Ying-Ying Zhang ◽  
Xiao-Qing Jin
Keyword(s):  
Differential Equation ◽  
Theoretical Analysis ◽  
Convergence Rate ◽  
Option Pricing ◽  
Gradient Method ◽  
Preconditioned Conjugate Gradient ◽  
Superlinear Convergence Rate ◽  
Pricing Problems ◽  
Toeplitz Systems ◽  
Toeplitz System

AbstractWe consider a nonsymmetric Toeplitz system which arises in the discretization of a partial integro-differential equation in option pricing problems. The preconditioned conjugate gradient method with a tri-diagonal preconditioner is used to solve this system. Theoretical analysis shows that under certain conditions the tri-diagonal preconditioner leads to a superlinear convergence rate. Numerical results exemplify our theoretical analysis.

Power Systems Investments

2011 ◽  
pp. 248-267
Author(s):  
João Zambujal-Oliveira
Keyword(s):  
Monte Carlo ◽  
Brownian Motion ◽  
Power Systems ◽  
Option Pricing ◽  
Real Options ◽  
Geometric Brownian Motion ◽  
Real Options Approach ◽  
Pricing Problems ◽  
Recursive Solutions ◽  
Poor Adhesion

The study employs a real options approach that doesn’t need to capture all the uncertainty and proposes a process that directly determines the uncertainty associated with the first period. The results support that its use can be considered fair. However, it shows that long periods of operation and poor adhesion to the geometric Brownian motion by the project returns might call into question its use in the energy market. The values for option pricing have remained inside acceptable ranges, but some shortfalls could be found. First, the study employs Monte Carlo simulations, which can be viewed as forward-looking processes, and option pricing problems need backward recursive solutions. Second, the study shows that its simplicity produces results as accurate as those gathered from approaches with added complexity and computational needs.

Option bounds

2004 ◽  
Vol 41 (A) ◽  
pp. 145-156 ◽  
Author(s):  
Victor H. De La Peña ◽  
Rustam Ibragimov ◽  
Steve Jordan
Keyword(s):  
Option Pricing ◽  
Absolutely Continuous ◽  
Sharp Estimates ◽  
Monte Carlo Techniques ◽  
Option Pricing Model ◽  
Pricing Problems ◽  
Modelling Assumptions ◽  
Option Bounds ◽  
Expected Payoffs ◽  
Entire Distribution

In this paper, we obtain sharp estimates for the expected payoffs and prices of European call options on an asset with an absolutely continuous price in terms of the price density characteristics. These techniques and results complement other approaches to the derivative pricing problem. Exact analytical solutions to option-pricing problems and to Monte-Carlo techniques make strong assumptions on the underlying asset's distribution. In contrast, our results are semi-parametric. This allows the derivation of results without knowing the entire distribution of the underlying asset's returns. Our results can be used to test different modelling assumptions. Finally, we derive bounds in the multiperiod binomial option-pricing model with time-varying moments. Our bounds reduce the multiperiod setup to a two-period setting, which is advantageous from a computational perspective.

scholarly journals AN ADAPTIVE METHOD FOR EVALUATING MULTIDIMENSIONAL CONTINGENT CLAIMS: PART II

2003 ◽  
Vol 06 (04) ◽  
pp. 327-353 ◽  
Author(s):  
LARS O. DAHL
Keyword(s):  
Monte Carlo ◽  
Option Pricing ◽  
Variance Reduction ◽  
Adaptive Method ◽  
Unit Cube ◽  
Random Numbers ◽  
Quasi Monte Carlo ◽  
Low Discrepancy Sequences ◽  
Pricing Problems ◽  
Simulation Results

This is part two of a work on adaptive integration methods aimed at multidimensional option pricing problems in finance. It presents simulation results of an adaptive method developed in the companion article [3] for the evaluation of multidimensional integrals over the unit cube. The article focuses on a rather general test problem constructed to give insights in the success of the adaptive method for option pricing problems. We establish a connection between the decline rate of the ordered eigenvalues of the pricing problem and the efficiency of the adaptive method relative to the non-adaptive. This gives criteria for when the adaptive method can be expected to outperform the non-adaptive for other pricing problems. In addition to evaluating the method for different problem parameters, we present simulation results after adding various techniques to enhance the adaptive method itself. This includes using variance reduction techniques for each sub-problem resulting from the partitioning of the integration domain. All simulations are done with both pseudo-random numbers and quasi-random numbers (low discrepancy sequences), resulting in Monte Carlo (MC) and quasi-Monte Carlo (QMC) estimators and the ability to compare them in the given setting. The results show that the adaptive method can give performance gains in the order of magnitudes for many configurations, but it should not be used incautious, since this ability depends heavily on the problem at hand.

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