scholarly journals Comparison of Black–Scholes Model and Monte-Carlo Simulation on Stock Price Modeling

2019 ◽  
Author(s):  
Qiwu Jiang*
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Stock Price ◽  
Black Scholes Model ◽  
Black Scholes

THE PRICING OF EXOTIC OPTIONS BY MONTE–CARLO SIMULATIONS IN A LÉVY MARKET WITH STOCHASTIC VOLATILITY

2003 ◽  
Vol 06 (08) ◽  
pp. 839-864 ◽  
Author(s):  
WIM SCHOUTENS ◽  
STIJN SYMENS
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Stochastic Volatility ◽  
Stock Price ◽  
Poisson Approximation ◽  
Exotic Options ◽  
Option Prices ◽  
Compound Poisson Approximation ◽  
Black Scholes ◽  
Cliquet Options

Recently, stock price models based on Lévy processes with stochastic volatility were introduced. The resulting vanilla option prices can be calibrated almost perfectly to empirical prices. Under this model, we will price exotic options, like barrier, lookback and cliquet options, by Monte–Carlo simulation. The sampling of paths is based on a compound Poisson approximation of the Lévy process involved. The precise choice of the terms in the approximation is crucial and investigated in detail. In order to reduce the standard error of the Monte–Carlo simulation, we make use of the technique of control variates. It turns out that there are significant differences with the classical Black–Scholes prices.

scholarly journals A Comparative Study of Pricing Option with Efficient Methods

2021 ◽  
pp. 1-7
Author(s):  
Sujon Chandra Sutradhar ◽  
ABM Shahadat Hossain
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Stock Price ◽  
Computer Algebra System ◽  
Numerical Technique ◽  
Science And Engineering ◽  
Merton Model ◽  
Pricing Options ◽  
Black Scholes ◽  
And Behavior

Our main objective of this paper is to introduce four individual techniques of pricing options; the techniques are Binomial method, Trinomial method, Monte Carlo simulation and Black-Scholes-Merton model. Because they play a significant role in option valuation of stock price dynamics, risk managements as well as stock market. In this paper, we briefly discuss all these four methods with their properties and behavior. We also focused on numerical technique for the higher accuracy of option pricing and compare them graphically. We use the Computer Algebra System (CAS) Python (Edition 2019.3.1) for this purpose. GUB JOURNAL OF SCIENCE AND ENGINEERING, Vol 7, Dec 2020 P 1-7

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).

Valuation Method of Equity Incentives of Listed Companies Based on the Black-Scholes Model

2020 ◽  
Vol 12 (2) ◽  
pp. 36-49
Author(s):  
Zhongwen Liu ◽  
Yifei Chen
Keyword(s):  
Stock Price ◽  
Turnover Rate ◽  
Garch Model ◽  
Listed Companies ◽  
Valuation Method ◽  
Black Scholes Model ◽  
Black Scholes ◽  
S Model ◽  
The Garch Model ◽  
Equity Incentive

This article applies the classic Black-Scholes model (i.e. B-S model) and turnover rate adapted B-S model (revised B-S model) to equity incentive valuation of listed companies. Unlike other studies on equity incentive valuation which generally adopt historical volatility, this article applies the GARCH model to equity incentive valuation. The volatility of stock price is estimated by the GARCH model to improve the accuracy of equity incentive valuation. The turnover rate has an important impact on the equity incentive valuation of listed companies. Considering the turnover rate can improve the accuracy of the equity incentive valuation and reduce the error of equity incentive valuation. Through the case study of the equity incentive valuation of Infinova, the practicality of the equity incentive valuation method is further verified.

scholarly journals The Extended Black-Scholes Model with-LAGS-and “Hedging Errors”

2003 ◽  
Author(s):  
Mondher Bellalah
Keyword(s):  
Stock Price ◽  
Standard Form ◽  
Small Time ◽  
Market Model ◽  
Short Term ◽  
Hedging Strategy ◽  
Underlying Asset ◽  
Elapsed Time ◽  
Black Scholes Model ◽  
Black Scholes

The Black-Scholes model is derived under the assumption that heding is done instantaneously. In practice, there is a “small” time that elapses between buying or selling the option and hedging using the underlying asset. Under the following assumptions used in the standard Black-Scholes analysis, the value of the option will depend only on the price of the underlying asset S, time t and on other Variables assumed constants. These assumptions or “ideal conditions” as expressed by Black-Scholes are the following. The option us European, The short term interest rate is known, The underlying asset follows a random walk with a variance rate proportional to the stock price. It pays no dividends or other distributions. There is no transaction costs and short selling is allowed, i.e. an investment can sell a security that he does not own. Trading takes place continuously and the standard form of the capital market model holds at each instant. The last assumption can be modified because in practice, trading does not take place in-stantaneouly and simultaneously in the option and the underlying asset when implementing the hedging strategy. We will modify this assumption to account for the “lag”. The lag corresponds to the elapsed time between buying or selling the option and buying or selling - delta units of the underlying assets. The main attractions of the Black-Scholes model are that their formula is a function of “observable” variables and that the model can be extended to the pricing of any type of option. All the assumptions are conserved except the last one.

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 Exotic Options Using Some Lattice Procedures

2021 ◽  
Vol 41 (1) ◽  
pp. 26-40
Author(s):  
Sadia Anjum Jumana ◽  
ABM Shahadat Hossain
Keyword(s):  
Stock Price ◽  
Lattice Models ◽  
Exotic Options ◽  
Barrier Options ◽  
Tree Model ◽  
Binomial Tree ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Binomial Tree Model ◽  
Trinomial Tree Model

In this work, we discuss some very simple and extremely efficient lattice models, namely, Binomial tree model (BTM) and Trinomial tree model (TTM) for valuing some types of exotic barrier options in details. For both these models, we consider the concept of random walks in the simulation of the path which is followed by the underlying stock price. Our main objective is to estimate the value of barrier options by using BTM and TTM for different time steps and compare these with the exact values obtained by the benchmark Black-Scholes model (BSM). Moreover, we analyze the convergence of these lattice models for these exotic options. All the results have been shown numerically as well as graphically. GANITJ. Bangladesh Math. Soc.41.1 (2021) 26-40

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