/AppliedTimeSeriesAnalysisProject

📈This final project was part of the Applied Time Series And Analysis course held in THU (2022)

Primary LanguageR

Project Report

Applied Time Series Analysis - THU

Participants

Name, Surname: Evgeniy Petrov

Name, Surname: Jonas Bezler

Submission Date: 05.12.2022

Exercise Descriptions

Exercise 1

In the csv file dataset<your group number>.csv you have saved a data set, but you forgot the theoretic process you’ve used for generating it. Can you reproduce the formula using your advanced time series skills?

Exercise 2

You’ll also find two stock price data

a. Load the data sets to R and perform an adequate preprocessing. Test for missing values and outliers. We’re using the close prices.

b. Which of the two stock prices would you consider as riskier? And why? Elaborate!

c. Choose one of the stocks (any preferences?), and compute the 95% VaR for 4 months in advance. How reliable is this number? Any criticism? Any possible solutions?

Exercise 3

Again choose one of the two stock price data. We intend to gamble a bit and expect increasing prices. A European call option would be the right tool for it. We’ve briefly discussed the option during the lecture. Let me please define it again. Let’s assume a strike price S which is 10% above the last noted price P. Let’s denote the last observed price by $P_{T}$. Then the European Call option value for a so called time-to-maturity of k is given as

$$E(max(\left( P_{T + k} - S \right);0)$$

Please estimate the option value using price simulations for a k of 60.

Hint: You need a simulation of the absolute prices, but you probably simulate the differences or log-differences. How to reconstruct the absolute prices from them?. Simply consider if $r_{t}\ : = logX_{t + 1} - logX_{t}$ then $X_{t + 1} = X_{t}e^{r_{t}}$ . So if you have simulations for the returns you can reconstruct simulations for the absolute prices.

Exercise Solutions

Check out the uploaded .dox file 🙂