scholarly journals Pricing barrier and barrier crack option under levy process

2021 ◽  
Author(s):  
Rofeide Jabbari
Keyword(s):  
Monte Carlo ◽  
Lévy Process ◽  
Oil And Gas ◽  
Real Data ◽  
Levy Process ◽  
Gasoline Prices ◽  
The Monte Carlo Method ◽  
Black Scholes ◽  
Gas Market ◽  
Computation Speed

In this thesis we study and analyze the pricing of barrier and barrier crack options under a Time-Changed Levy process. Oil and gasoline in Canada are our underlying commodities of interest in this study. To characterize the dynamics of oil and gasoline prices, Black-Scholes and Time-Changed models based on Levy process are proposed. To verify the model, real data of the Canada oil and gas market is used. While the pricing methods based on Monte Carlo are the well-known and dominant for price calculation, we propose a Fourier Transform (FT) for the pricing, which provide some important advantages to the Monte Carlo method such as computation speed without compromising any accuracy. The method is also applied to Crack spread contracts to reduce the risk.

scholarly journals Pricing barrier and barrier crack option under levy process

2021 ◽  
Author(s):  
Rofeide Jabbari
Keyword(s):  
Monte Carlo ◽  
Lévy Process ◽  
Oil And Gas ◽  
Real Data ◽  
Levy Process ◽  
Gasoline Prices ◽  
The Monte Carlo Method ◽  
Black Scholes ◽  
Gas Market ◽  
Computation Speed

In this thesis we study and analyze the pricing of barrier and barrier crack options under a Time-Changed Levy process. Oil and gasoline in Canada are our underlying commodities of interest in this study. To characterize the dynamics of oil and gasoline prices, Black-Scholes and Time-Changed models based on Levy process are proposed. To verify the model, real data of the Canada oil and gas market is used. While the pricing methods based on Monte Carlo are the well-known and dominant for price calculation, we propose a Fourier Transform (FT) for the pricing, which provide some important advantages to the Monte Carlo method such as computation speed without compromising any accuracy. The method is also applied to Crack spread contracts to reduce the risk.

Markov Chain Monte Carlo simulation of the distribution of some perpetuities

1999 ◽  
Vol 31 (01) ◽  
pp. 112-134 ◽  
Author(s):  
Jostein Paulsen ◽  
Arne Hove
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Lévy Process ◽  
Sufficient Conditions ◽  
Random Variable ◽  
Levy Process ◽  
Present Value ◽  
Strong Markov

We study the present value Z ∞ = ∫0 ∞ e-X t- dY t where (X,Y) is an integrable Lévy process. This random variable appears in various applications, and several examples are known where the distribution of Z ∞ is calculated explicitly. Here sufficient conditions for Z ∞ to exist are given, and the possibility of finding the distribution of Z ∞ by Markov chain Monte Carlo simulation is investigated in detail. Then the same ideas are applied to the present value Z - ∞ = ∫0 ∞ exp{-∫0 t R s ds}dY t where Y is an integrable Lévy process and R is an ergodic strong Markov process. Numerical examples are given in both cases to show the efficiency of the Monte Carlo methods.

scholarly journals Prediksi Tingkat Pemahaman Siswa terhadap Data Nominatif Menggunakan Metode Monte Carlo

2020 ◽  
pp. 90-95
Author(s):  
Lc Granadi Suhaidir ◽  
S Sumijan ◽  
Yuhandri Yunus
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Real Data ◽  
Trial Data ◽  
Manual Search ◽  
The Monte Carlo Method ◽  
Work Training ◽  
West Sumatra ◽  
Level Of Understanding ◽  
The City

Kerinci Regency which was established on November 10, 1957 from the results of the division of 3 provinces, namely West Sumatra Province, Riau Province, Jambi Province. The district which is nicknamed the City of Sakti Alam Kerinci has a population of 253,258 people with an area of ​​3,808 km and consists of 16 sub-districts. So that training, technology, and improving Maunisa Resources are needed in various aspects of Kerinci society. Determine the level of accuracy of the Monte Carlo method simulation between the simulation results and the real data. In this study, the main data used were data for 2017, 2018 and 2019. The variable used in this study was the frequency of student scores in participating in learning. The value data will be processed using the Monte Carlo method assisted by Microsoft Excel for manual search. Student grade data for 2017 is used as trial data to predict in 2018, data for 2018 is used as trial data to predict the number of 2019, and data for 2019 will be used to predict the number in 2020 later. Where the highest prediction result is 96% where there are several competencies that have the same value. So that the average resulting from the predicted accuracy is 95% of the 7 competencies. The test results have clearly formed the boundaries. With an accuracy rate of 95%, it can be recommended to help the UPTD Kerinci District Work Training Center in predicting the level of understanding of students.

scholarly journals Simulasi Monte Carlo dalam Prediksi Jumlah Penumpang Angkutan Massal Bus Rapid Transit Kota Padang

2020 ◽  
Author(s):  
Khaliq Alfikrizal ◽  
Sarjon Defit ◽  
Yuhandri Yunus
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Real Data ◽  
Bus Rapid Transit ◽  
Rapid Transit ◽  
High Quality ◽  
Simulation Data ◽  
The Monte Carlo Method ◽  
Average Accuracy ◽  
High Level

Bus Rapid Transit is a system of bus facilities, services and comfort which is used to increase speed and reliability and is integrated with a strong transit identity through high quality services. Trans Padang is a land transportation based on Bus Rapid Transit in Padang City which is managed by the Transportation Agency which started operating in January 2014 with a total bus fleet of 10 units on the Lubuk Buaya-Pasar Raya Padang route. Currently it has 2 corridors operating out of 6 corridors designed. This study aims to predict the number of Bus Rapid Transit passengers in Padang City and determine the level of accuracy of simulation data with real data using the Monte Carlo method. The data used to predict the number of passengers is data on the number of passengers from January 2017 to December 2019. From the simulations carried out, simulated accuracy is obtained for predicting the number of passengers with an average accuracy of above 80%. Based on a fairly high level of accuracy, the application of the Monte Carlo method to predict the number of Bus Rapid Transit passengers in Padang City is considered to be able to predict the number of passengers in the following year.

scholarly journals Error Bounds for Small Jumps of Lévy Processes

2013 ◽  
Vol 45 (1) ◽  
pp. 86-105
Author(s):  
E. H. A. Dia
Keyword(s):  
Monte Carlo ◽  
Brownian Motion ◽  
Error Bounds ◽  
Monte Carlo Methods ◽  
Lévy Process ◽  
Lévy Processes ◽  
Levy Processes ◽  
Levy Process ◽  
Lévy Measure ◽  
Exponential Lévy Models

The pricing of options in exponential Lévy models amounts to the computation of expectations of functionals of Lévy processes. In many situations, Monte Carlo methods are used. However, the simulation of a Lévy process with infinite Lévy measure generally requires either truncating or replacing the small jumps by a Brownian motion with the same variance. We will derive bounds for the errors generated by these two types of approximation.

Markov Chain Monte Carlo simulation of the distribution of some perpetuities

1999 ◽  
Vol 31 (1) ◽  
pp. 112-134 ◽  
Author(s):  
Jostein Paulsen ◽  
Arne Hove
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Markov Chain ◽  
Markov Chain Monte Carlo ◽  
Lévy Process ◽  
Sufficient Conditions ◽  
Random Variable ◽  
Levy Process ◽  
Present Value ◽  
Strong Markov

We study the present value Z∞ = ∫0∞ e-Xt-dYt where (X,Y) is an integrable Lévy process. This random variable appears in various applications, and several examples are known where the distribution of Z∞ is calculated explicitly. Here sufficient conditions for Z∞ to exist are given, and the possibility of finding the distribution of Z∞ by Markov chain Monte Carlo simulation is investigated in detail. Then the same ideas are applied to the present value Z-∞ = ∫0∞ exp{-∫0tRsds}dYt where Y is an integrable Lévy process and R is an ergodic strong Markov process. Numerical examples are given in both cases to show the efficiency of the Monte Carlo methods.

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.

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