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 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

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.

The Financial Clouds Review

2012 ◽  
pp. 1062-1083 ◽  
Author(s):  
Victor Chang ◽  
Chung-Sheng Li ◽  
David De Roure ◽  
Gary Wills ◽  
Robert John Walters ◽  
...  
Keyword(s):  
Cloud Computing ◽  
Monte Carlo ◽  
Least Square ◽  
Software As A Service ◽  
Special Technique ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Speed Accuracy ◽  
Financial Software ◽  
Business Framework

This paper demonstrates financial enterprise portability, which involves moving entire application services from desktops to clouds and between different clouds, and is transparent to users who can work as if on their familiar systems. To demonstrate portability, reviews for several financial models are studied, where Monte Carlo Methods (MCM) and Black Scholes Model (BSM) are chosen. A special technique in MCM, Least Square Methods, is used to reduce errors while performing accurate calculations. Simulations for MCM are performed on different types of Clouds. Benchmark and experimental results are presented for discussion. 3D Black Scholes are used to explain the impacts and added values for risk analysis. Implications for banking are also discussed, as well as ways to track risks in order to improve accuracy. A conceptual Cloud platform is used to explain the contributions in Financial Software as a Service (FSaaS) and the IBM Fined Grained Security Framework. This study demonstrates portability, speed, accuracy, and reliability of applications in the clouds, while demonstrating portability for FSaaS and the Cloud Computing Business Framework (CCBF).

The Financial Clouds Review

2013 ◽  
pp. 125-146
Author(s):  
Victor Chang ◽  
Chung-Sheng Li ◽  
David De Roure ◽  
Gary Wills ◽  
Robert John Walters ◽  
...  
Keyword(s):  
Cloud Computing ◽  
Monte Carlo ◽  
Least Square ◽  
Software As A Service ◽  
Special Technique ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Speed Accuracy ◽  
Financial Software ◽  
Business Framework

This paper demonstrates financial enterprise portability, which involves moving entire application services from desktops to clouds and between different clouds, and is transparent to users who can work as if on their familiar systems. To demonstrate portability, reviews for several financial models are studied, where Monte Carlo Methods (MCM) and Black Scholes Model (BSM) are chosen. A special technique in MCM, Least Square Methods, is used to reduce errors while performing accurate calculations. Simulations for MCM are performed on different types of Clouds. Benchmark and experimental results are presented for discussion. 3D Black Scholes are used to explain the impacts and added values for risk analysis. Implications for banking are also discussed, as well as ways to track risks in order to improve accuracy. A conceptual Cloud platform is used to explain the contributions in Financial Software as a Service (FSaaS) and the IBM Fined Grained Security Framework. This study demonstrates portability, speed, accuracy, and reliability of applications in the clouds, while demonstrating portability for FSaaS and the Cloud Computing Business Framework (CCBF).

scholarly journals Impurity lattice Monte Carlo for hypernuclei

2020 ◽  
Vol 56 (10) ◽  
Author(s):  
Dillon Frame ◽  
Timo A. Lähde ◽  
Dean Lee ◽  
Ulf-G. Meißner
Keyword(s):  
Field Theory ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Effective Field Theory ◽  
Computational Effort ◽  
Effective Field ◽  
Binding Energies ◽  
Chiral Effective Field Theory ◽  
Lattice Monte Carlo ◽  
Nucleon Interactions

AbstractWe consider the problem of including $$\varLambda $$ Λ hyperons into the ab initio framework of nuclear lattice effective field theory. In order to avoid large sign oscillations in Monte Carlo simulations, we make use of the fact that the number of hyperons is typically small compared to the number of nucleons in the hypernuclei of interest. This allows us to use the impurity lattice Monte Carlo method, where the minority species of fermions in the full nuclear Hamiltonian is integrated out and treated as a worldline in Euclidean projection time. The majority fermions (nucleons) are treated as explicit degrees of freedom, with their mutual interactions described by auxiliary fields. This is the first application of the impurity lattice Monte Carlo method to systems where the majority particles are interacting. Here, we show how the impurity Monte Carlo method can be applied to compute the binding energies of the light hypernuclei. In this exploratory work we use spin-independent nucleon–nucleon and hyperon–nucleon interactions to test the computational power of the method. We find that the computational effort scales approximately linearly in the number of nucleons. The results are very promising for future studies of larger hypernuclear systems using chiral effective field theory and realistic hyperon–nucleon interactions, as well as applications to other quantum many-body systems.

A Binary Option Pricing Based on Fuzziness

2014 ◽  
Vol 13 (06) ◽  
pp. 1211-1227 ◽  
Author(s):  
Masatoshi Miyake ◽  
Hiroshi Inoue ◽  
Jianming Shi ◽  
Tetsuya Shimokawa
Keyword(s):  
Monte Carlo ◽  
Option Pricing ◽  
Primary Role ◽  
Pricing Model ◽  
European Option ◽  
Over The Counter ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Fuzzy Boundary

In pricing for European option Black–Scholes model has been widely used in various fields in which the model can be applied under appropriate conditions. In this paper, we discuss a binary option, which is popular in OTC (Over the Counter) market for hedging and speculation. In particular, asset-or-nothing option is basic for any other options but gives essential implications for constructing more complex option products. In addition to the primary role of the asset-or-nothing option, another availability of the option is considered by introducing fuzzy concept. Therefore, the uncertainty which an investor and intermediary usually have in their minds is incorporated in the pricing model. Thus, the model is described with fuzzy boundary conditions and applied to the conventional binary option, proposing more useful and actual pricing way of the option. This methodology with the analysis is examined, comparing with Monte Carlo simulations.

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