scholarly journals Monte Carlo Methods and New Jump Diffusion Processes and Their Application in Gold Price

2017 ◽  
Author(s):  
Kutluk Kağan Sümer
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Standard Deviation ◽  
Diffusion Process ◽  
Wiener Process ◽  
Mean Reversion ◽  
Jump Diffusion ◽  
Gold Market ◽  
Jump Diffusion Process ◽  
Standard Deviations

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.

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

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.

A theoretical model of jump diffusion-mean reversion

2017 ◽  
Vol 23 (3) ◽  
pp. 537-554
Author(s):  
Anindya Chakrabarty ◽  
Zongwei Luo ◽  
Rameshwar Dubey ◽  
Shan Jiang
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Theoretical Model ◽  
Interest Rate ◽  
Mean Reversion ◽  
Jump Diffusion ◽  
Fixed Income ◽  
Short Term ◽  
Content Type ◽  
Better Than

Purpose The purpose of this paper is to develop a theoretical model of a jump diffusion-mean reversion constant proportion portfolio insurance strategy under the presence of transaction cost and stochastic floor as opposed to the deterministic floor used in the previous literatures. Design/methodology/approach The paper adopts Merton’s jump diffusion (JD) model to simulate the price path followed by risky assets and the CIR mean reversion model to simulate the path followed by the short-term interest rate. The floor of the CPPI strategy is linked to the stochastic process driving the value of a fixed income instrument whose yield follows the CIR mean reversion model. The developed model is benchmarked against CNX-NIFTY 50 and is back tested during the extreme regimes in the Indian market using the scenario-based Monte Carlo simulation technique. Findings Back testing the algorithm using Monte Carlo simulation across the crisis and recovery phases of the 2008 recession regime revealed that the portfolio performs better than the risky markets during the crisis by hedging the downside risk effectively and performs better than the fixed income instruments during the growth phase by leveraging on the upside potential. This makes it a value-enhancing proposition for the risk-averse investors. Originality/value The study modifies the CPPI algorithm by re-defining the floor of the algorithm to be a stochastic mean reverting process which is guided by the movement of the short-term interest rate in the economy. This development is more relevant for two reasons: first, the short-term interest rate changes with time, and hence the constant yield during each rebalancing steps is not practically feasible; second, the historical literatures have revealed that the short-term interest rate tends to move opposite to that of the equity market. Thereby, during the bear run the floor will increase at a higher rate, whereas the growth of the floor will stagnate during the bull phase which aids the model to capitalize on the upward potential during the growth phase and to cut down on the exposure during the crisis phase.

scholarly journals PENENTUAN NILAI PREMI ASURANSI PERTANIAN PADA KOMODITAS KOPI BERBASIS HARGA INTERNASIONAL MENGGUNAKAN MODEL MEAN REVERSION DENGAN LOMPATAN

2017 ◽  
Vol 6 (4) ◽  
pp. 253
Author(s):  
INTAN LESTARI ◽  
KOMANG DHARMAWAN ◽  
DESAK PUTU EKA NILAKUSMAWATI
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Production Cost ◽  
Mean Reversion ◽  
Jump Diffusion ◽  
Insurance Premium ◽  
Agricultural Insurance ◽  
Premium Payment ◽  
International Prices ◽  
Search Data

Agricultural insurance with the interantional price is new insurance in Indonesia. The international insurance premium is given if the international prices lower than the determined trigger value. The purpose of this study is to presents the steps needed to determine the premium value of the agricultural insurance. The steps are to search data of the international prices and local prices commodity coffee, calculate the return of both data, calculate descriptive statistic, calculate correlation between international prices of commodity coffee and local prices commodity coffee, estimate the parameter by using Maksimum Likelihood Estimasi(MLE), to do the Monte Carlo simulation by using Mean Reversion with Jump Diffusion, to determine the production cost, normality log test, to determine the trigger indexs, and to count the premium value with put cash-or-nothing option. On this study if international prices lower than the determined trigger value, trigger payments as much as Rp 20.248.282,4/Ha based on trigger index as many Rp 24.900/kg, so amount of premium payment equals Rp 334.000.

scholarly journals Monte Carlo method to valuate CAT bonds of flood in Surabaya under Jump Diffusion Process

2021 ◽  
Vol 1821 (1) ◽  
pp. 012026
Author(s):  
Hengky Kurniawan ◽  
Endah RM Putri ◽  
Chairul Imron ◽  
Dedy D. Prastyo
Keyword(s):  
Monte Carlo ◽  
Monte Carlo Method ◽  
Diffusion Process ◽  
Jump Diffusion ◽  
Cat Bonds ◽  
Jump Diffusion Process

scholarly journals Solutions to the jump-diffusion linear stochastic differential equations

2019 ◽  
Vol 3 (2) ◽  
pp. 115-119
Author(s):  
Dang Kien Cuong ◽  
Duong Ton Dam ◽  
Duong Ton Thai Duong ◽  
Du Thuan Ngo
Keyword(s):  
Differential Equations ◽  
Diffusion Process ◽  
Stochastic Differential Equations ◽  
Wiener Process ◽  
Lévy Process ◽  
Random Measure ◽  
Jump Diffusion ◽  
Continuous Functions ◽  
Levy Process ◽  
Jump Diffusion Process

The jump-diffusion stochastic process is one of the most common forms in reality (such as wave propagation, noise propagation, turbulent flow, etc.), and researchers often refer to them in models of random processes such as Wiener process, Levy process, Ito-Hermite process, in research of G. D. Nunno, B. Oksendal, F. B. Hanson, etc. In our research, we have reviewed and solved three problems: (1) Jump-diffusion process (also known as the Ito-Levy process); (2) Solve the differential equation jump-diffusion random linear, in the case of one-dimensional; (3) Calculate the Wiener-Ito integral to the random Ito-Hermite process. The main method for dealing with the problems in our presentation is the Ito random-integrable mathematical operations for the continuous random process associated with the arbitrary differential jump by the Poisson random measure. This study aims to analyse the basic properties of jump-diffusion process that are solutions to the jump-diffusion linear stochastic differential equations: dX(t) = [a (t)X (t􀀀)+A(t)]dt + [b (t)X (t􀀀 ∫ )+B(t)]dW (t) + R0 [g (t; z)X (t􀀀)+G(t; z)] ¯N (dt;dz) with a set of stochastic continuous functions fa;b ;g ;A;B;Gg and assuming that the compensated Poisson process ¯N (t; z) is independent of the Wiener process W(t). Derived from the Ito-Hermite formulas for the Ito-Hermite process and for the Ito-Levy process class we presented the results for the differential and multiple stochastic integration for the Ito- Hermite process. We also provided a separation method to solve jump-diffusion linear differential equations.  

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