scholarly journals A Benchmark Approach of Counterparty Credit Exposure of Bermudan Option under Lévy Process: The Monte Carlo-COS Method

2013 ◽  
Vol 18 ◽  
pp. 1163-1171 ◽  
Author(s):  
Yanbin Shen ◽  
J.A.M. Van Der Weide ◽  
J.H.M. Anderluh
Keyword(s):  
Monte Carlo ◽  
Lévy Process ◽  
Levy Process ◽  
Bermudan Option ◽  
Benchmark Approach

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 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 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.

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 (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.

scholarly journals Error Bounds for Small Jumps of Lévy Processes

2013 ◽  
Vol 45 (01) ◽  
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.

scholarly journals LAN property for a simple Lévy process

2014 ◽  
Vol 352 (10) ◽  
pp. 859-864 ◽  
Author(s):  
Arturo Kohatsu-Higa ◽  
Eulalia Nualart ◽  
Ngoc Khue Tran
Keyword(s):  
Lévy Process ◽  
Levy Process
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