# Quantitative Finance and Economics Lecture 5: Descriptive Statistics

This lecture of quantitative finance and economics covers descriptive statistics.

## 1  Lecture Slides

R Descriptive Statistics Examples

R Examples: Descriptive Statistics Examples for Daily Dataownload PDF slides

R codes: descriptiveStatistics.r

# Quantitative Finance and Economics Lecture 4: Time Series Conceipts

This lecture of quantitative finance and economics covers some basic conceipts of time series.

## 1  Lecture Slides

R Time Series Examples

R codes: timeSeriesConcepts.r

# Quantitative Finance and Economics Lecture 3: Matrix Algebra

This lecture of quantitative finance and economics covers matrix algebra.

## 1  Lecture Slides

R Matrix Examples

matrixReview.xlsx

R codes: matrixReview.r

# Pricing Options Lecture 4: Pricing In Discrete Time Models

This pricing options lecture covers pricing in discrete time models.

# Pricing Options Lecture 3: No-arbitrage Pricing Relations

This pricing options lecture covers some no-arbitrage pricing relations.

# Stochastic Calculus Notes 3: Brownian Motion

This?note of stochastic calculus covers Brownian motion and its basic properties.

## 1  Random Walks

### 1.1  Symmetric random walk

#### 1.1.1  Definition

Let be a successive outcomes of the fair coin toss experiment (). Let’s define a random variable

and define , then we can construct following process , which is called a symmetric random walk.

With each toss, this process either steps up one unit or down one unit, and each of the two possibilities is equally likely.

# Stochastic Calculus Notes 2: Information and Conditioning

This note of stochastic calculus covers mathematical descriptions of information and conditioning.

## 1  Information

### 1.1  Background

In dynamic hedging, the position of underlying security at each future time is contigent on how the uncertainty between the present time and that future time is resolved. In order to make contingency plans, we need a way to mathematically model the information on which future decisions can be based.

A discrete example:

• We imagine some random experiment is performed. We denote as the set of all possible outcomes, and denote as one particular outcome.
• Suppose we are given some information. Such information is not enough to tell the exact value of , but is enough for us to narrow down the possibilities. Specifically, based on such given information, we can construct a list of sets of outcomes, called the sets resolved by the information, within which we know what sets are sure to contain and what other sets are sure not to contain it.
• At each time, the list of sets resolved from the given information form a σ-algebra, so we obtain a series of σ-sigma, , indexed by time. As time moves forward, we obtain finer resolution, meaning that contains more information than  for any .
• Above collection of σ-algebra, , is an example of a filtration.

Below is the definition of infiltration in the continuous-time sense. Read more Stochastic Calculus Notes 2: Information and Conditioning

# Pricing Options Lecture 2: Interest Rates, Forward Rates, Bond Yields

This pricing options lecture covers onterest rates, forward rates, and bond yields.

# Pricing Options Lecture 1: Stocks, Bonds, Derivatives

This pricing options lecture covers stocks, bonds, and derivatives.

# Quantitative Finance and Economics Lecture 2: Probability Review

This lecture of quantitative finance and economics presents some basic reviews of probability.

## 1  Lecture Slides

Lecture slides, Part 1

Lecture slides, Part 2

R Probability Examples

probReview.xls

R codes: probReview.r

## 2  Introduction-1 (1:06)

In this lecture we begin our review of probability theory. We will learn about random variables and distribution functions for discrete and continuous random variables. Particular attention will be paid to the normal distribution and its use in financial modeling. We will also discuss the shape characteristics of distributions such as expected value, standard deviation, skewness and kurtosis. Finally, we define the risk concept, Value-at-Risk, and how it relates to the quantiles of a distribution. These probability concepts will serve as a foundation for the rest of the course.