This paper analyses the implementation and calibration of the Heston Stochastic Volatility Model. We first introduce the model, provides theoretical motivation for its robustness and hence popularity and explain how characteristic functions can be used to estimate option prices. Then we consider the implementation of the Heston model, showing that relatively simple solutions can lead to fast and accurate currency option prices. In this work, we perform several tests, using both local and global calibration to evaluate the Predictive Accuracy of the Heston Stochastic Volatility Model for currency options.Our analyses show that straightforward setups deliver excellent calibration results. All calculations are carried out in MATLAB and included in the paper. All the MATLAB’s codes required to implement the model are provided in the appendix A.

Since the sixties, debates have been born on the models, which determine the evolution of the stock prices. In this work we will focus on one of the best performances in the region of the Middle East and North Africa (MENA), is Africa's third largest Bourse: Casablanca Stock Exchange (CSE), which had the “Index de la Bourse des Valeurs de Casablanca” (IGB) as an index. IGB was replaced in January 2002 by two indexes: MASI (Moroccan All Shares Index) comprises all listed shares, allows investors to follow all listed values and to have a long-term visibility. MADEX (Moroccan Most Active Shares Index) comprises most active shares listed continuously with variations closely linked to all the market serves as a reference for the listing of all funds invested in shares.Firstly, it aims at the investigation of stochastic model to show the variation of MASI index values, and, secondly, we will achieve a prediction interval of 95% of chance for Moroccan index future values. Here, the geometric Brownian motion (stochastic process without mean reversion propriety) is used to model the stochastic variation of MASI index values. In order to calculate models’ parameters daily close values of the Moroccan index from 02/01/2003 to 05/11/2019 can be taken from Casablanca Stock Exchange and, hence, stochastic models for MASI index variation is to be derived.

Exchange rate in Moroccan economy has been considered a critical push-forward force for domestic inflation which leads to the depreciation of currency value. Exchange rate is the price for which the currency of a country can be exchanged for another country's currency in the foreign exchange market. This article seeks to adopt two stochastic models for estimation of exchange rate EURO/MAD. Firstly, it aims at the investigation of stochastic models (two models) to show the variation of exchange rate, and, secondly, try to draw a comparison between these models in terms of error estimation performances and, as a result, to recommend a stochastic model for exchange rate EURO/MAD. The present paper is an extension of our precedent work entitled and referenced: “Elaboration of two stochastic models of EURO/MAD exchange rate and measure of their forecast accuracy,” International Journal of Innovation and Applied Studies, vol. 17, no. 3, pp. 1029–1036, August 2016.. In addition to our precedent results (for reasons of clarity we repeat our previous work here), we produced a prediction intervals for each future value of exchange rate EURO/MAD. In this paper, the geometric Brownian motion (stochastic process without mean reversion propriety) and Vasicek process (stochastic process with mean reversion speed), are used to model the exchange rate EURO / MAD, then they are compared in terms of average estimation error. In order to calculate models parameters daily close price of the Euro/MAD from 01/12/2008 to 01/03/2016 (2242 values) can be taken from Casablanca stock exchange and ,hence, two stochastic models for exchange rate is to be derived, and compared. According to simulation results, we can finally recommend one of the two models.

Exchange rate in Moroccan economy has been considered a critical push-forward force for domestic inflation which leads to the depreciation of currency value. Exchange rate is the price for which the currency of a country can be exchanged for another country's currency in the foreign exchange market. This article seeks to adopt two stochastic models for estimation of exchange rate EURO/MAD. Firstly, it aims at the investigation of stochastic models (two models) to show the variation of exchange rate, and, secondly, try to draw a comparison between these models in terms of error estimation performances and, as a result, to recommend a stochastic model for exchange rate EURO/MAD. In this paper, the geometric Brownian motion (stochastic process without mean reversion propriety) and Vasicek process (stochastic process with mean reversion speed), are used to model the exchange rate EURO / MAD, then they are compared in terms of average estimation error. In order to calculate models parameters daily close price of the Euro/MAD from 01/12/2008 to 01/03/2016 (2242 values) can be taken from Casablanca stock exchange and ,hence, two stochastic models for exchange rate is to be derived, and compared. According to simulation results, we can finally recommend one of the two models.