Efficient Monte Carlo Barrier Option Pricing When the Underlying Security Price Follows a Jump-Diffusion Process

This study aimed to execute Monte Carlo simulation method with Wiener Process, Generalized Wiener Process, Mean Reversion Process and Mean Reversion Jump Diffusion Process and to compare them and then expended with the idea of how to include negative and positive news shocks in the gold market to the Monte Carlo simulation. By enhancing the determination of the 3 standard deviation shocks within the process of Classic Mean Jump Diffusion Process, an enchanted model for the 1,96 and 3 standard deviation shocks were being used and additionally positive and negative shocks were added to the system in a different way. This new Mean Reversion Jump Diffusion Process that have been developed by Sümer, executes Monte Carlo simulation regarding the gold market return with five random variables that are chosen from Poisson distribution and one random variable chosen from the normal distribution. Additionally, by accepting volatilities as outlies over the 1,96 and 3 standard deviations with the effect of the new and good news and the standard deviations on the traditional approximate return and the standard deviations (volatility) and the obtained new approximate return and the new standard deviation (volatility) and compares them with the Monte Carlo simulations.

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Option Pricing under the Jump Diffusion and Multifactor Stochastic Processes

Journal of Function Spaces ◽

10.1155/2019/9754679 ◽

2019 ◽

Vol 2019 ◽

pp. 1-12 ◽

Cited By ~ 3

Author(s):

Shican Liu ◽

Yanli Zhou ◽

Yonghong Wu ◽

Xiangyu Ge

Keyword(s):

Diffusion Process ◽

Option Pricing ◽

Stochastic Volatility ◽

Term Structure ◽

Implied Volatility ◽

Jump Diffusion ◽

Stochastic Volatility Model ◽

Heston Model ◽

Volatility Model ◽

Jump Diffusion Process

In financial markets, there exists long-observed feature of the implied volatility surface such as volatility smile and skew. Stochastic volatility models are commonly used to model this financial phenomenon more accurately compared with the conventional Black-Scholes pricing models. However, one factor stochastic volatility model is not good enough to capture the term structure phenomenon of volatility smirk. In our paper, we extend the Heston model to be a hybrid option pricing model driven by multiscale stochastic volatility and jump diffusion process. In our model the correlation effects have been taken into consideration. For the reason that the combination of multiscale volatility processes and jump diffusion process results in a high dimensional differential equation (PIDE), an efficient finite element method is proposed and the integral term arising from the jump term is absorbed to simplify the problem. The numerical results show an efficient explanation for volatility smirks when we incorporate jumps into both the stock process and the volatility process.

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Jump Adapted Scheme Of a Non Mark Dependent Jump Diffusion Process with Application to the Merton Jump Diffusion Model

International Journal of Statistics and Probability ◽

10.5539/ijsp.v6n4p80 ◽

2017 ◽

Vol 5 (4) ◽

pp. 80

Author(s):

Renaud Fadonougbo ◽

George O. Orwa

Keyword(s):

Monte Carlo Simulation ◽

Monte Carlo ◽

Diffusion Process ◽

Strong Convergence ◽

General Result ◽

Jump Diffusion ◽

Discretization Scheme ◽

Complete Proof ◽

Jump Diffusion Process ◽

Jump Diffusion Model

This paper provides a complete proof of the strong convergence of the Jump adapted discretization Scheme in the univariate and mark independent jump diffusion process case. We put in detail and clearly a known and general result for mark dependent jump diffusion process. A Monte-Carlo simulation is used as well to show numerical evidence.

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