A simulation framework for investigating the market scenarios of the forex market using Ornstein-Uhlenbeck and Monte-Carlo simulation

Abstract

The forex market is a financial market that is a global marketplace for exchanging national currencies. Forex investment is generally mediated by a broker and executed by a trader. Thereby, the investment scenarios are based on realistic exchange price fluctuations and the best market representations. Herein, all possible combinations of upward-downward movement of the exchange rate fluctuations have been considered as scenarios. However, the exchange rates have three parts namely, selling price, buying price, and absolute exchange rate, making the framework rather complex. The three price series have to be simulated focusing on the market behaviors and particular exchange rate patterns alongside price regulations undertaken by the respective authorities. As the literature suggests, in such a scenario modeling, the currency historical data analysis may not be prominent as the currency profiles have less memory dependency. Thus, in the determination of possible scenarios, memory-less stochastic processes are more appropriate than memory-depending stochastic processes. This study investigated the possibility of forming such a realistic simulation framework using appropriate mathematical tools. The exchange rates of currencies are highly volatile. The literature has illustrated that the OrnsteinUhlenbeck (OU) process shows a reliable representation of such exchange rate profiles. Thereby, this analysis focused on OU simulation representing the exchange of major nine currency pairs. The respective OU process parameters were identified based on historical data. However, parameter optimization was conducted at the level of stochastic process expectation. Thus, the Monte Carlo procedure is used in parameter estimation and has been utilized in scenario analysis as well. The respective realizations of these identified OU processes have been utilized in modeling the possible exchange rate representations and scenario simulations. As an example, the three series of USD-EURO exchange rates are simulated by the OU process with the identified parameters based on their respective historical data. A Monte-Carlo is used to formed to analyze desired strategies alongside the perspectives of brokers and traders. Using the simulation framework, we have tested the price fluctuations for traders and brokers to ensure they are realistic based on exchange rate data. The results have illustrated that brokers get the optimum profit. The profit of each process has been calculated for the broker, and the expected profit has also been calculated. Not only that, changing the parameters (mean and volatility) from 0.0001 to 0.0006 also got the expected values to check how the profits vary in that situation. After each process space was stable, identified strategies to get more profit from the broker's perspective. Finally, the strategies from the trader’s perspective were identified to get more profit while assuming there was only one trader. Also, the same process was done 1000 times and got traders an expected profit. Through the application of simulation tools, this research contributes to the current discussion about successful trading tactics in this changing environment.