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 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 Analysis of the Black-Scholes- Merton Model and the Heston Stochastic Volatility Model

2019 ◽  
Vol 39 ◽  
pp. 127-140
Author(s):  
Tahmid Tamrin Suki ◽  
ABM Shahadat Hossain
Keyword(s):  
Comparative Analysis ◽  
Stochastic Volatility ◽  
Stock Prices ◽  
Computer Algebra System ◽  
Stochastic Volatility Model ◽  
Affecting Factors ◽  
Pricing Models ◽  
Merton Model ◽  
Volatility Model ◽  
Black Scholes

This paper compares the performance of two different option pricing models, namely, the Black-Scholes-Merton (B-S-M) model and the Heston Stochastic Volatility (H-S-V) model. It is known that the most popular B-S-M Model makes the assumption that volatility of an asset is constant while the H-S-V model considers it to be random. We examine the behavior of both B-S-M and H-S-V formulae with the change of different affecting factors by graphical representations and hence assimilate them. We also compare the behavior of some of the Greeks computed by both of these models with changing stock prices and hence constitute 3D plots of these Greeks. All the numerical computations and graphical illustrations are generated by a powerful Computer Algebra System (CAS), MATLAB. GANIT J. Bangladesh Math. Soc.Vol. 39 (2019) 127-140

scholarly journals Prediction of Stock Price Movements using Monte Carlo Simulation

2019 ◽  
Vol 8 (12) ◽  
pp. 2012-2016
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Stock Price ◽  
Narrow Band ◽  
Share Price ◽  
Share Prices ◽  
The Past ◽  
Price Movements ◽  
A Minor ◽  
Random Behaviour

Monte Carlo Simulation depends on random behaviour of events. When a variable takes values at random and becomes highly unpredictable due to its nature of randomness, the property of random numbers is made use of for predicting the future values that the variable may take. This property can be made use of for predicting share price movements, when the past share prices exhibit random behaviour, without exhibiting high fluctuations. This article explains the methodology of using Monte Carlo Simulation for predicting share price movements and explains the process with the help of an illustration taking the monthly share price data of ITC Limited for a period of 36 months, where the share prices have moved within a narrow band. Findings of the analysis show that it works well and that the method of prediction is reasonably accurate, showing only a minor deviation from the actual prices.

VARIANCE GAMMA PROCESS WITH MONTE CARLO SIMULATION AND CLOSED FORM APPROACH FOR EUROPEAN CALL OPTION PRICE DETERMINATION

2021 ◽  
Vol 14 (2) ◽  
pp. 183-193
Author(s):  
Abdul Hoyyi ◽  
Abdurakhman Abdurakhman ◽  
Dedi Rosadi
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Closed Form ◽  
Stock Price ◽  
Option Price ◽  
Secondary Data ◽  
Exponential Model ◽  
Variance Gamma ◽  
Variance Gamma Process ◽  
Normally Distributed

The Option is widely applied in the financial sector.  The Black-Scholes-Merton model is often used in calculating option prices on a stock price movement. The model uses geometric Brownian motion which assumes that the data is normally distributed. However, in reality, stock price movements can cause sharp spikes in data, resulting in nonnormal data distribution. So we need a stock price model that is not normally distributed. One of the fastest growing stock price models today is the  process exponential model. The  process has the ability to model data that has excess kurtosis and a longer tail (heavy tail) compared to the normal distribution. One of the members of the  process is the Variance Gamma (VG) process. The VG process has three parameters which each of them, to control volatility, kurtosis and skewness. In this research, the secondary data samples of options and stocks of two companies were used, namely zoom video communications, Inc. (ZM) and Nokia Corporation (NOK).  The price of call options is determined by using closed form equations and Monte Carlo simulation. The Simulation was carried out for various  values until convergent result was obtained.

A NEW MONTE CARLO METHOD FOR AMERICAN OPTIONS

2004 ◽  
Vol 07 (05) ◽  
pp. 591-614 ◽  
Author(s):  
G. N. MILSTEIN ◽  
O. REIß ◽  
J. SCHOENMAKERS
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Monte Carlo Method ◽  
Boundary Value Problem ◽  
Numerical Experiments ◽  
American Options ◽  
American Option ◽  
Parabolic Boundary ◽  
Black Scholes ◽  
Exercise Boundary

We introduce a new Monte Carlo method for constructing the exercise boundary of an American option in a generalized Black–Scholes framework. Based on a known exercise boundary, it is shown how to price and hedge the American option by Monte Carlo simulation of suitable probabilistic representations in connection with the respective parabolic boundary value problem. The method presented is supported by numerical experiments.

scholarly journals Stock Price Simulation Using Bootstrap and Monte Carlo

2017 ◽  
Vol 64 (2) ◽  
pp. 155-170 ◽  
Author(s):  
Martin Pažický
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Stock Price ◽  
Error Term ◽  
Monte Carlo Experiment ◽  
Asian Option ◽  
Heteroscedastic Error ◽  
Maturity Date ◽  
The Future ◽  
The Difference

Abstract In this paper, an attempt is made to assessment and comparison of bootstrap experiment and Monte Carlo experiment for stock price simulation. Since the stock price evolution in the future is extremely important for the investors, there is the attempt to find the best method how to determine the future stock price of BNP Paribas′ bank. The aim of the paper is define the value of the European and Asian option on BNP Paribas′ stock at the maturity date. There are employed four different methods for the simulation. First method is bootstrap experiment with homoscedastic error term, second method is blocked bootstrap experiment with heteroscedastic error term, third method is Monte Carlo simulation with heteroscedastic error term and the last method is Monte Carlo simulation with homoscedastic error term. In the last method there is necessary to model the volatility using econometric GARCH model. The main purpose of the paper is to compare the mentioned methods and select the most reliable. The difference between classical European option and exotic Asian option based on the experiment results is the next aim of tis paper.

Local Monte Carlo Simulation for the Reliability Sensitivity Analysis

2011 ◽  
Vol 291-294 ◽  
pp. 2183-2188 ◽  
Author(s):  
Da Wei Li ◽  
Zhen Zhou Lu ◽  
Zhang Chun Tang
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Numerical Technique ◽  
Limit State ◽  
Computational Cost ◽  
Simulation Method ◽  
State Function ◽  
Local Domain ◽  
Monte Carlo Simulation Method ◽  
Reliability Sensitivity

An efficient numerical technique, namely the Local Monte Carlo Simulation method, is presented to assess the reliability sensitivity in this paper. Firstly some samples are obtained by the random sampling, then the local domain with a constant probability content corresponding to each sample point can be defined, finally the conditional reliability and reliability sensitivity corresponding to every local region can be calculated by using linear approximation of the limit state function. The reliability and reliability sensitivity can be estimated by the expectation of all the conditional reliability and reliability sensitivity. Three examples testify the applicability, validity and accuracy of the proposed method. The results computed by the Local Monte Carlo Simulation method and the Monte Carlo method are compared, which demonstrates that, without losing precision, the computational cost by the former method is much less than the later.

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