Modelación y pronóstico de la TRM a partir de un modelo de saltos de difusión, un modelo de Black and Scholes y un modelo ARIMA, así como la comparación de los resultados de pronóstico entre ellos.

Abstract

In this project the reader will learn about different concepts related to foreign exchange market, mainly currencies. It will be explained the history of the currencies market, kinds of operations in this market such as types of currencies that market participants could find. Also, there will be described the exchange parity for Colombia and its characteristics. Likewise, there Will be a brief summary about inherent market risks like volatility, local regulation and some international definitions from different authors and a view froem Basel Agreements I and II. In the same way, it will be exposed different techniques to measure market risk, particularly, Value at Risk. On the other hand, it will be shown different kinds of derivatives, definition of volatility and how to measure it, different probability distributions which will be used for model estimation such as Bernoulli or Binomial Distribution. In addition, another statistical definition such like kurtosis or Jarque-Bera test, which is used to test normality in a time serie. Talking about models, it will be elucidated, models like Black and Scholes model, Jump diffusion model, ARIMA model. Finally, there is written the methodology to create the model using different staff said above such as Jarque-Bera test. Further there are the results and some final comments and considerations.