Analysis of Options Pricing Methods: the Black-Scholes Model and the Monte-Carlo Method

2020 ◽  
Vol 9 (3) ◽  
pp. 39-42
Author(s):  
Leysen Yunusova
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Investment Decisions ◽  
Estimation Methods ◽  
Options Pricing ◽  
Financial Instruments ◽  
Strategic Investment ◽  
Black Scholes Model ◽  
The Monte Carlo Method ◽  
Black Scholes

Currently, the market of financial instruments is quite developed. Traditional financial instruments prevail on the Russian market, while derivatives of these financial instruments (options, futures, forwards, bills, etc.) are faintly developed. The reason for this situation is that few participants in the financial market can correctly evaluate financial products. Scientific researchers and large companies use different methods of estimating the value of financial instruments in making strategic investment decisions, since incorrect calculations can be irreparable. Therefore, it is important to apply the appropriate pricing methodology to various derivative financial instruments. The topic of derivative financial instruments in terms of scientific and theoretical aspects has been worked out in sufficient volume, but as for the pricing of these instruments, there are some gaps. There is still no method for pricing derivatives that would allow you to accurately assess the value of financial instruments for subsequent effective investment decisions. In this article considers the methodology of pricing of derivative financial instruments using the Black-Scholes model and the Monte Carlo method. The presented estimation methods allow us to calculate the range of price values that allows us to provide the most accurate expected results.

scholarly journals Pricing Basket Options by Polynomial Approximations

2021 ◽  
Author(s):  
Pablo Olivares ◽  
Alexander Alvarez
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Closed Form ◽  
Computational Effort ◽  
Basket Options ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Power Moments ◽  
Exponential Power ◽  
Closed Form Approximation

We propose a closed-form approximation for the price of basket options under a multivariate Black-Scholes model. The method is based on Taylor and Chebyshev expansions and involves mixed exponential-power moments of a Gaussian distribution. Our numerical results show that both approaches are comparable in accuracy to a standard Monte Carlo method, with a lesser computational effort

scholarly journals Pricing Basket Options by Polynomial Approximations

2016 ◽  
Vol 2016 ◽  
pp. 1-12 ◽  
Author(s):  
Pablo Olivares ◽  
Alexander Alvarez
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Closed Form ◽  
Computational Effort ◽  
Basket Options ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Power Moments ◽  
Exponential Power ◽  
Closed Form Approximation

We propose a closed-form approximation for the price of basket options under a multivariate Black-Scholes model. The method is based on Taylor and Chebyshev expansions and involves mixed exponential-power moments of a Gaussian distribution. Our numerical results show that both approaches are comparable in accuracy to a standard Monte Carlo method, with a lesser computational effort.

scholarly journals Analysis of economic-financial viability, by the monte carlo method, in service provider of non-destructible tests: case study

2020 ◽  
Vol 11 (4) ◽  
pp. 1454
Author(s):  
Vanessa Miguel Augusto Souza ◽  
Nilson Brandalise
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Net Present Value ◽  
Investment Decisions ◽  
Internal Rate Of Return ◽  
Present Value ◽  
The Monte Carlo Method ◽  
A Company ◽  
Non Destructive

This work aims to present the economic-financial feasibility, through the application of the Monte Carlo Method, to assist managers in the decision making regarding the investment of a service contract of a company specialized in Non-Destructive Tests, with the tests of Penetrant Liquid and Ultrasound, to which the company that takes the service establishes the requirements previously. The method was apply, in 5000 iterations, from the established parameters, for the initial investment and demand of the test diaries, which provided data regarding the average for the Net Present Value (NPV), Internal Rate of Return (IRR) and Profitability Index (PI), as well as the possible standard deviations, established by the coefficient of variation. Finally, after analyzing the data, it was check that the Method is useful to assist in the making of investment decisions, being feasible the adherence of the contract studied, through the analyzed data and established criteria.

scholarly journals Pricing Basket Options by Polynomial Approximations

2021 ◽  
Author(s):  
Pablo Olivares ◽  
Alexander Alvarez
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Closed Form ◽  
Computational Effort ◽  
Basket Options ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Power Moments ◽  
Exponential Power ◽  
Closed Form Approximation

We propose a closed-form approximation for the price of basket options under a multivariate Black-Scholes model. The method is based on Taylor and Chebyshev expansions and involves mixed exponential-power moments of a Gaussian distribution. Our numerical results show that both approaches are comparable in accuracy to a standard Monte Carlo method, with a lesser computational effort

UGR CALCULATION BASED ON THE LUMINANCE SPATIAL-ANGULAR DISTRIBUTION

2020 ◽  
Vol 2020 (4) ◽  
pp. 25-32
Author(s):  
Viktor Zheltov ◽  
Viktor Chembaev
Keyword(s):  
Monte Carlo ◽  
Angular Distribution ◽  
Monte Carlo Method ◽  
Visual Task ◽  
New Method ◽  
Lighting System ◽  
Preliminary Assessment ◽  
System A ◽  
The Monte Carlo Method

The article has considered the calculation of the unified glare rating (UGR) based on the luminance spatial-angular distribution (LSAD). The method of local estimations of the Monte Carlo method is proposed as a method for modeling LSAD. On the basis of LSAD, it becomes possible to evaluate the quality of lighting by many criteria, including the generally accepted UGR. UGR allows preliminary assessment of the level of comfort for performing a visual task in a lighting system. A new method of "pixel-by-pixel" calculation of UGR based on LSAD is proposed.

PSHA software review based on the Monte Carlo method

2020 ◽  
pp. 14-24
Author(s):  
V.A. Mironov ◽  
S.A. Peretokin ◽  
K.V. Simonov
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Seismic Hazard ◽  
Hazard Analysis ◽  
Software Review ◽  
Seismic Hazard Analysis ◽  
Probabilistic Seismic Hazard ◽  
Test Calculation ◽  
Seismic Surveys ◽  
The Monte Carlo Method

The article is a continuation of the software research to perform probabilistic seismic hazard analysis (PSHA) as one of the main stages in engineering seismic surveys. The article provides an overview of modern software for PSHA based on the Monte Carlo method, describes in detail the work of foreign programs OpenQuake Engine and EqHaz. A test calculation of seismic hazard was carried out to compare the functionality of domestic and foreign software.

Application of the Monte Carlo Method for the Prediction of Behavior of Peptides

2019 ◽  
Vol 20 (12) ◽  
pp. 1151-1157 ◽  
Author(s):  
Alla P. Toropova ◽  
Andrey A. Toropov
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Natural Sciences ◽  
Monte Carlo Technique ◽  
Quantitative Structure ◽  
Structure Property ◽  
The Monte Carlo Method ◽  
Modern Natural

Prediction of physicochemical and biochemical behavior of peptides is an important and attractive task of the modern natural sciences, since these substances have a key role in life processes. The Monte Carlo technique is a possible way to solve the above task. The Monte Carlo method is a tool with different applications relative to the study of peptides: (i) analysis of the 3D configurations (conformers); (ii) establishment of quantitative structure – property / activity relationships (QSPRs/QSARs); and (iii) development of databases on the biopolymers. Current ideas related to application of the Monte Carlo technique for studying peptides and biopolymers have been discussed in this review.

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