The Monte Carlo method is one of the most powerful mathematical techniques that, through calculation, analyzes risk and allows solving physical and mathematical problems through computer programs, Using historical data, creates and predicts models of possible future results by substituting a range of values, calculating results over and over again, using a different group of random values of the probability functions to predict the possible results of some uncertain event related to problems of all kinds.

Monte Carlo simulations offer a clearer picture than a deterministic forecast. The model has a wide range of applications that offer the probability of possible outcomes in various sectors that handle multiple random variables such as business, investment, engineering, biology, meteorology, astronomy, particle physics, etc. Among the practical applications in business, finance, and economics, we can mention the following problems:

The development of the Monte Carlo method began in 1946 by the mathematician and physicist Stanislaw Ulam (1909-1984), who was involved in the Manhattan Project whose objective was to develop the first atomic bomb. The idea of statistical simulation arose after asking the following question: What is the possibility of successfully solving a Canfield solitaire with 52 cards? The method was built thinking about problems such as neutron diffusion in mathematical physics. and in how to change the processes by differential equations as a succession of random operations. This idea was shared with John Von Neumann, and together they began to plan the actual calculations. (^{Ulam, 1983}).

In the Journal of the American Statistical Association, in 1949 a seminal article was published where Nicholas Metropolis and Stanislaw Ulam presented the technique: The Monte Carlo method. The name Monte Carlo to designate the statistical simulation technique was proposed by Metropolis, inspired by the interest that Stanislaw Ulam had in the game of poker, (^{Metropolis and Stanislaw, 1949}).

The Monte Carlo method is a numerical resolution method where the relationships and interactions of different objects and their environment are modeled, through the random generation of these interactions. The greater the repetition of tests, the result that converges to a value with greater precision. (^{Vargas & Cruz-Carpio, 2020})

In Monte Carlo methods the properties of the distributions of random variables are investigated by simulating random numbers. These methods are like the usual statistical methods in which random samples are used to make inferences about source populations. In its statistical application, a model is used to simulate a phenomenon that contains some random component. In Monte Carlo methods, the object of investigation is a model itself, and random or pseudo-random events are used to study it (^{Gentle, 2006}).

In all types of research where an observation or measurement experiment is carried out, and data from different variables are obtained; It is essential to make a dependency relationship between the variables to make predictions or forecasts of future events.

The difference between a simulation and a statistical analysis is that in the Monte Carlo simulation, the results or output variables previously obtained in the statistical analysis are used as input variables (^{Eppen, 2000}).

At present, the Monte Carlo model methodology has not been applied in armed conflicts, its use has been oriented towards solving problems to obtain a social benefit. The great importance of the Monte Carlo method is based on the attention to problems that are difficult to solve by analytical or numerical methods, which depend on random factors or are associated with a deterministic model, identifying, and offering optimal solutions.

Economic and financial indicators are useful tools that benefit organizations by facilitating timely and appropriate decision-making about their corporate and financial strategies.

Next, the evolution of some economic and financial indicators of the Mexican environment is described and shown to facilitate decision-making related to personal and business strategies in an integral manner.

1.NATIONAL CONSUMER PRICE INDEX (INPC)

Born in 1995 and reflecting changes in consumer prices, measures the general increase in prices in the country. It is calculated fortnightly by the Bank of Mexico and INEGI (2021). INPC is published in the Official Gazette of the Federation on the 10th and 25th of each month. The reference period is the second half of December 2010.

Table 1 Accumulated inflation in the year (Base: 2nd. Fortnight of December 2010 = 100 with data provided by Banco de México) 

Periodo	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020	2021	2022	2023
Enero	1.48	0.77	0.98	0.79	0.90	-0.09	0.38	1.70	0.53	0.09	0.48	0.86	0.59	0.76
Febrero	2.15	1.42	1.47	1.46	1.15	0.09	0.82	2.29	0.91	0.06	0.90	1.50	1.43	1.24
Marzo	2.52	1.84	1.55	1.99	1.43	0.51	0.97	2.92	1.24	0.44	0.85	2.34	2.43	1.51
Abril	1.98	0.72	0.69	1.81	1.24	0.25	0.65	3.04	0.90	0.50	-0.17	2.67	2.98	1.47
Mayo	0.60	-0.70	-0.65	0.95	0.91	-0.26	0.20	2.92	0.73	0.21	0.22	2.88	3.17	1.27
Junio	0.49	-0.41	-0.41	1.12	1.09	-0.09	0.31	3.18	1.12	0.27	0.76	3.43	4.04	1.37
Julio	0.56	-0.04	0.32	1.14	1.42	0.06	0.57	3.57	1.66	0.65	1.43	4.04	4.81	1.86
Agosto	0.91	0.30	0.92	1.31	1.73	0.27	0.86	4.08	2.26	0.63	1.82	4.24	5.54	2.42
Septiembre	1.27	0.73	1.12	1.61	2.18	0.27	1.47	4.41	2.69	0.89	2.06	4.88	6.19
Octubre	2.35	2.33	2.12	2.77	2.74	1.16	2.09	5.06	3.22	1.44	2.68	5.76	6.79
Noviembre	3.89	4.87	3.86	4.57	3.57	1.71	2.89	6.15	4.10	2.26	2.76	6.97	7.41
Diciembre	4.19	5.81	3.97	5.21	4.08	2.13	3.36	6.77	4.83	2.83	3.15	7.35	7.82

Source: Own elaboration (^{INEGI, 2023}). Route: Indicadores económicos de coyuntura > Índices de precios > Índice nacional de precios al consumidor. Base segunda quincena de julio de 2018=100 > Mensual > Índice > Índice general

Source: Own elaboration (^{INEGI, 2023}). Route: Indicadores económicos de coyuntura > Índices de precios > Índice nacional de precios al consumidor. Base segunda quincena de julio de 2018=100 > Mensual > Índice > Índice general

Graph 1 Inflation in Mexico (2010-2022 accumulated at the end of the year) 

Source: Own elaboration (^{INEGI, 2023}). Route: Indicadores económicos de coyuntura > Índices de precios > Índice nacional de precios al consumidor. Base segunda quincena de julio de 2018=100 > Mensual > Índice > Índice general

Graph 2 Inflation in Mexico (accumulated January-August 2023) 

2.THE PRICE AND QUOTATION INDEX OF THE MEXICAN STOCK EXCHANGE (IPC)

Represents the change in the values traded on the Mexican Stock Exchange concerning the previous day to determine the percentage of rising or falling of the most representative shares of the companies listed therein.

Table 2 The Price and Quotation Index of the Mexican Stock Exchange (Base: October 1978, 0.78=100) 

2011	2012	2013	2014	2015	2016	2017	2018	2019	2020	2021	2022	2023
36,982	37,422	45,278	40,879	40,951	43,631	47,001	50,456	43,988	44,862	42,986	51,331	54,564
37,020	37,816	44,121	38,783	44,190	43,715	46,857	47,438	42,824	41,324	44,593	53,401	52,758
37,441	39,521	44,077	40,462	43,725	45,881	48,542	46,125	43,281	34,554	47,246	56,537	53,904
36,963	39,461	42,263	40,712	44,582	45,785	49,261	48,354	44,597	36,470	48,010	51,418	55,121
35,833	37,872	41,588	41,363	44,704	45,459	48,788	44,663	42,749	36,122	50,886	51,753	52.736
36,558	40,199	40,623	42,737	45,054	45,966	49,857	47,663	43,161	37,716	50,290	47,524	53.526
35,999	40,704	40,838	43,818	44,753	46,661	51,012	49,698	40,863	37,020	50,868	48,144	54.819
35,721	39,422	39,492	45,628	43,722	47,541	51,210	49,548	42,623	36,841	53,305	44,919	53.021
33,503	40,867	40,185	44,986	42,633	47,246	50,346	49,504	43,011	37,459	51,386	44,627
36,160	41,620	41,039	45,028	44,543	48,009	48,626	43,943	43,337	36,988	51,310	49,922
36,829	41,834	42,499	44,190	43,419	45,286	47,092	41,733	42,820	41,779	49,699	51,685
37,077	43,706	42,727	43,146	42,998	45,643	49,354	41,640	43,541	44,067	53,272	48,464

Source: Own elaboration (^{BANXICO, 2023}). https://www.banxico.org.mx/SieInternet/consultarDirectorioInternetAction.do?sector=7&accion=consultarCuadro&idCuadro=CF57&locale=es

Source: Own elaboration (^{BANXICO, 2023}). https://www.banxico.org.mx/SieInternet/consultarDirectorioInternetAction.do?sector=7&accion=consultarCuadro&idCuadro=CF57&locale=es

Graph 3 The Price and Quotation Index of the Mexican Stock Exchange, 2011 - 2022 (Score at the end of each year) 

Source: Own elaboration (^{BANXICO, 2023}). https://www.banxico.org.mx/SieInternet/consultarDirectorioInternetAction.do?sector=7&accion=consultarCuadro&idCuadro=CF57&locale=es

Graph 4 The Price and Quotation Index of the Mexican Stock Exchange, January-August 2023 (Score at the end of each month 

3.EXCHANGE RATE

It is the value of the Mexican peso concerning the dollar calculated with the daily average of the five most important banks in the country, which reflects the spot price (cash), negotiated between banks. It is highly related to Inflation, the interest rate, and the Mexican Stock Exchange.

Table 3 Exchange rate (National currency per US dollar, parity at the end of each period) 

Periodo	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020	2021	2022	2023
Enero	12.02	12.95	12.71	13.37	14.69	18.45	21.02	18.62	19.04	18.91	20.22	20.74	18.79
Febrero	12.17	12.87	12.87	13.30	14.92	18.17	19.83	18.65	19.26	19.78	20.94	20.65	18.34
Marzo	11.97	12.80	12.36	13.08	15.15	17.40	18.81	18.33	19.38	23.48	20.44	19.99	18.04
Abril	11.59	13.20	12.16	13.14	15.22	19.40	19.11	18.86	19.01	23.93	20.18	20.57	18.00
Mayo	11.63	13.91	12.63	12.87	15.36	18.45	18.51	19.75	19.64	22.18	19.92	19.69	17.74
Junio	11.84	13.66	13.19	13.03	15.57	18.91	17.90	20.06	19.21	23.09	19.91	20.13	17.07
Julio	11.65	13.28	12.73	13.06	16.21	18.86	17.69	18.55	19.99	22.20	19.85	20.34	16.73
Agosto	12.41	13.27	13.25	13.08	16.89	18.58	17.88	19.07	20.07	21.89	20.06	20.09	16.92
Septiembre	13.42	12.92	13.01	13.45	17.01	19.50	18.13	18.90	19.68	22.14	20.56	20.09
Octubre	13.20	13.09	12.89	13.42	16.45	18.84	19.15	19.80	19.16	21.25	20.53	19.82
Noviembre	14.03	13.04	13.09	13.72	16.55	20.55	18.58	20.41	19.61	20.14	21.45	19.40
Diciembre	13.99	13.01	13.08	14.72	17.21	20.73	19.79	19.68	18.87	19.91	20.47	19.47

NOTE: Exchange rate FIX by The Banco de México, used for settle obligations denominated in foreign currency. Quote at the end

Source: Own elaboration (^{BANXICO, 2023}). https://www.banxico.org.mx/SieInternet/consultarDirectorioInternetAction.do?sector=6&accion=consultarCuadro&idCuadro=CF102&locale=es

Source: Own elaboration (^{BANXICO, 2023}). https://www.banxico.org.mx/SieInternet/consultarDirectorioInternetAction.do?sector=6&accion=consultarCuadro&idCuadro=CF102&locale=es

Graph 5 Exchange rate (National currency per US dollar, 2011-2022, FIX parity at the end of each year) 

Source: Own elaboration (^{BANXICO, 2023}). https://www.banxico.org.mx/SieInternet/consultarDirectorioInternetAction.do?sector=6&accion=consultarCuadro&idCuadro=CF102&locale=es

Graph 6 Exchange rate (National currency per US dollar, January-August 2023, FIX parity at the end of each month) 

4.EQUILIBRIUM INTERBANK INTEREST RATE (TIIE)

On March 23, 1995, the Bank of Mexico, to establish an interbank interest rate that better reflects market conditions, released the Interbank Equilibrium Interest Rate through the Official Gazette of the Federation.

Table 4 Equilibrium interbank interest rate (28-day quote) 

Periodo	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020	2021	2022	2023
Enero	4.91	4.86	4.79	4.84	3.78	3.29	3.56	6.15	7.66	8.59	7.50	4.47	5.72	10.78
Febrero	4.92	4.84	4.78	4.80	3.79	3.29	4.05	6.61	7.83	8.54	7.29	4.36	6.02	11.10
Marzo	4.92	4.84	4.77	4.35	3.81	3.30	4.07	6.68	7.85	8.51	6.74	4.28	6.33	11.34
Abril	4.94	4.85	4.75	4.33	3.80	3.30	4.07	6.89	7.85	8.50	6.25	4.28	6.73	11.53
Mayo	4.94	4.85	4.76	4.30	3.79	3.30	4.10	7.15	7.86	8.51	5.74	4.29	7.01	11.54
Junio	4.94	4.85	4.77	4.31	3.31	3.30	4.11	7.36	8.10	8.49	5.28	4.32	7.42	11.50
Julio	4.92	4.82	4.78	4.32	3.31	3.31	4.59	7.38	8.11	8.47	5.19	4.52	8.04	11.50
Agosto	4.90	4.81	4.79	4.30	3.30	3.33	4.60	7.38	8.10	8.26	4.76	4.65	8.50	11.50
Septiembre	4.90	4.78	4.81	4.03	3.29	3.33	4.67	7.38	8.12	8.04	4.55	4.75	8.89
Octubre	4.87	4.79	4.83	3.78	3.28	3.30	5.11	7.38	8.15	7.97	4.51	4.98	9.56
Noviembre	4.87	4.80	4.85	3.80	3.31	3.32	5.57	7.39	8.34	7.78	4.48	5.13	10.00
Diciembre	4.89	4.79	4.85	3.79	3.31	3.55	6.11	7.62	8.60	7.55	4.49	5.72	10.53

Source: Own elaboration (BANXICO, 2023). https://www.banxico.org.mx/SieInternet/consultarDirectorioInternetAction.do?sector=18&accion=c onsultarCuadro&idCuadro=CF101&locale=es

Source: Own elaboration (^{BANXICO, 2023}). https://www.banxico.org.mx/SieInternet/consultarDirectorioInternetAction.do?sector=18&accion=consultarCuadro&idCuadro=CF101&locale=es

Graph 7 Equilibrium interbank interest rate, 2010- 2022 (at the end of each year) 

Source: Own elaboration (^{BANXICO, 2023}). https://www.banxico.org.mx/SieInternet/consultarDirectorioInternetAction.do?sector=18&accion=consultarCuadro&idCuadro=CF101&locale=es

Graph 8 Equilibrium interbank interest rate, January-August 2023 (28-day quote) 

5.CETES RATE OF RETURN

Table 5 CETES rate of return (28-day) 

Periodo	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020	2021	2022	2023
Enero	4.49	4.14	4.27	4.15	3.14	2.67	3.08	5.83	7.25	7.95	7.04	4.22	5.50	10.80
Febrero	4.49	4.04	4.32	4.19	3.16	2.81	3.36	6.06	7.40	7.93	6.91	4.02	5.94	11.04
Marzo	4.45	4.27	4.24	3.98	3.17	3.04	3.80	6.32	7.47	8.02	6.59	4.08	6.52	11.34
Abril	4.44	4.28	4.29	3.82	3.23	2.97	3.74	6.50	7.46	7.78	5.84	4.06	6.68	11.27
Mayo	4.52	4.31	4.39	3.72	3.28	2.98	3.81	6.56	7.51	8.07	5.38	4.07	6.90	11.25
Junio	4.59	4.37	4.34	3.78	3.02	2.96	3.81	6.82	7.64	8.18	4.85	4.03	7.56	11.02
Julio	4.60	4.14	4.15	3.85	2.83	2.99	4.21	6.99	7.73	8.15	4.63	4.35	8.05	11.09
Agosto	4.52	4.05	4.13	3.84	2.77	3.04	4.24	6.94	7.73	7.87	4.50	4.49	8.35	11.07
Sep.	4.43	4.23	4.17	3.64	2.83	3.10	4.28	6.99	7.69	7.61	4.25	4.69	9.25
Oct.	4.03	4.36	4.21	3.39	2.90	3.02	4.69	7.03	7.69	7.62	4.22	4.93	9.00
Nov.	3.97	4.35	4.23	3.39	2.85	3.02	5.15	7.02	7.83	7.46	4.28	5.05	9.70
Dic.	4.30	4.34	4.05	3.29	2.81	3.14	5.61	7.17	8.02	7.25	4.24	5.49	10.10

Source: Own elaboration (^{BANXICO, 2023}). https://www.banxico.org.mx/SieInternet/consultarDirectorioInternetAction.do?sector=22&accion=consultarCuadro&idCuadro=CF107&locale=es

Source: Own elaboration (^{BANXICO, 2023}). https://www.banxico.org.mx/SieInternet/consultarDirectorioInternetAction.do?sector=22&accion=consultarCuadro&idCuadro=CF107&locale=es

Graph 9 CETES rate of return 2010- 2022 (at the end of each year) 

Source: Own elaboration (^{BANXICO, 2023}). https://www.banxico.org.mx/SieInternet/consultarDirectorioInternetAction.do?sector=22&accion=c onsultarCuadro&idCuadro=CF107&locale=es

Graph 10 CETES rate of return, January-August 2023 (at the end of each month) 

6.INVESTMENT UNITS (UDIS)

The UDI is a unit of account of constant real value to denominate credit titles. It does not apply to checks, commercial contracts, or other acts of commerce.

Table 6 Investment units (value concerning pesos) 

Periodo	2010	2011	2012	2013	2014	2015	2016	2017	2018	2019	2020	2021	2022	2023
Enero	4.37	4.56	4.73	4.89	5.10	5.29	5.41	5.62	5.97	6.25	6.44	6.64	7.12	7.69
Febrero	4.41	4.57	4.75	4.92	5.13	5.29	5.43	5.69	6.00	6.25	6.46	6.70	7.18	7.74
Marzo	4.44	4.59	4.75	4.94	5.15	5.30	5.44	5.71	6.02	6.26	6.49	6.75	7.24	7.77
Abril	4.46	4.59	4.75	4.97	5.15	5.32	5.45	5.75	6.03	6.28	6.43	6.79	7.31	7.78
Mayo	4.43	4.58	4.71	4.96	5.13	5.29	5.42	5.75	6.01	6.27	6.42	6.81	7.33	7,78
Junio	4.41	4.55	4.74	4.95	5.13	5.28	5.42	5.75	6.01	6.26	6.44	6.83	7.36	7.77
Julio	4.42	4.57	4.77	4.95	5.14	5.28	5.42	5.76	6.04	6.27	6.49	6.87	7.43	7.79
Agosto	4.43	4.58	4.78	4.95	5.16	5.29	5.44	5.79	6.07	6.29	6.52	6.90	7.47	7.83
Septiembre	4.44	4.59	4.80	4.97	5.18	5.31	5.45	5.82	6.11	6.29	6.55	6.92	7.53
Octubre	4.47	4.61	4.83	4.99	5.20	5.33	5.49	5.84	6.13	6.31	6.57	6.97	7.57
Noviembre	4.50	4.64	4.85	5.02	5.23	5.36	5.53	5.89	6.17	6.35	6.60	7.04	7.62
Diciembre	4.53	4.69	4.87	5.06	5.27	5.38	5.56	5.93	6.23	6.39	6.61	7.11	7.65

Source: Own elaboration (^{BANXICO, 2023}). https://www.banxico.org.mx/SieInternet/consultarDirectorioInternetAction.do?accion=consultarCuadro&idCuadro=CP150&locale=es

Source: Own elaboration (^{BANXICO, 2023}). https://www.banxico.org.mx/SieInternet/consultarDirectorioInternetAction.do?accion=consultarCuadro&idCuadro=CP150&locale=es

Graph 11 Investment units 2010-2022 (At the end of the year) 

Source: Own elaboration (^{BANXICO, 2023}). https://www.banxico.org.mx/SieInternet/consultarDirectorioInternetAction.do?accion=consultarCuadro&idCuadro=CP150&locale=es

Graph 12 Investment units, January-April 2023 

In these uncertain times, it is very important to apply the best mathematical models to carry out the appropriate analyzes that offer us the necessary information to make business decisions related, among others, to investment, opportunity costs, market share, sales forecasts, plans business, business valuation or risk assessment.