# Time series and mathematical finance

## Presentation

Time Series

1. Introduction and Descriptive Analysis
2. Random Modeling of Time Series
3. Statistical Inference of Stationary processes of order 2
4. ARMA and ARIMA Models

Mathematical Finance

This series of Lectures aims in providing the fundamental background in Corporate Finance and for deriving pricing and hedging formulae for derivatives based on discrete-time financial markets. More precisely, after a brief review of the vocabulary we will investigate the pricing and hedging of different types of securities such as bonds and  European (and American) derivatives in complete market models.

1. Corporate Finance : vocabulary
2. Notion of interest rate
3. A first pricing formula : the non-random framework
4. Discrete-time financial markets : a toy model
5. Discrete-time financial models : the general case
6. The Cox-Ross-Rubinstein market model
7. Pricing and hedging in incomplete markets : the superhedging approach
8. American Options

## Objectives

At the end of this lecture, the student should have acquired the following skills, as well theoretically than practically with the R statistical Software.

I)              Time series :

• Estimate or eliminate the trend and/or the seasonality of a time series
• Study the stationnarity of a time series
• Calculate and estimate the autocorrelogram and the autocorrelograms (total and partial) of a stationary process
• Study and/or adjust an ARMA (or ARIMA) model on a stationary time series
• Carry an optimal linear forecast of an ARMA process

II)             Mathematical Finance

At the end of this module, the student will have understood and be able to explain (main concepts):

The main concepts of Corporate Finance and of the Mathematical analysis of discrete-time Financial markets (such as the Cox-Ross-Rubinstein model).

The student will be able to:

Perform the pricing and the hedging of derivatives on discrete-time market models based on a deep understanding of the main mathematical concepts in Finance such as e.g. the notions of : arbitrage, portfolio, and equivalent martingale measure.

## Needed prerequisite

Probability and Statistics (MIC2) I2MIMT31

Statistics (MIC3) I3MIMT05

Probability and Inferential Statistics (I4MMMT21)

Martingales and Monte-Carlo Methods (GMM4) I4MMSP21

## Form of assessment

The evaluation of outcome prior learning is made as a continuous training during the semester. According ot the teaching, the assessment will be different: as a written exam, an oral exam, a record, a written report, peers review...