Quantitative Finance and Economics Lecture 5: Descriptive Statistics

This lecture of quantitative finance and economics covers descriptive statistics.

1  Lecture Slides 

Download PDF slides

R Descriptive Statistics Examples

R Examples: Descriptive Statistics Examples for Daily Dataownload PDF slides

R codes: descriptiveStatistics.r

 

2  Covariance Stationarity (11:28)

 

3  Histograms (11:33)

 

4  Sample Statistics (15:24)

 

5  Empirical CDF and QQ plots (12:00)

 

6  Outliers Part 1 (7:15)

 

7  Outliers Part 2 (7:39)

 

8  Descriptive Statistics for Daily Data (24:17)

 

 

Course Posts

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 

Download PDF slides

R Time Series Examples

R codes: timeSeriesConcepts.r

 

2  Time Series Concepts (16:48)

 

3  Autocorrelation (9:14)

 

4  White Noise Processes (12:31)

 

5  Nonstationary Processes (17:29)

 

6  Moving Average Processes (25:45)

 

7  Autoregressive Processes Part 1 (3:19)

 

8  Autoregressive Processes Part 2 (28:19)

 

 

Course Posts

Quantitative Finance and Economics Lecture 3: Matrix Algebra

This lecture of quantitative finance and economics covers matrix algebra.

1  Lecture Slides 

Download PDF slides

R Matrix Examples

matrixReview.xlsx

R codes: matrixReview.r

 

2  Matrix Algebra: Review Part 1 (17:02)

 

3  Matrix Algebra: Review Part 2 (20:10)

 

4  Further Instruction (2:11)

 

5  Matrix Algebra: Portfolio Math (21:14)

 

6  Matrix Algebra: Bivariate Normal (7:26)

 

 

Course Posts

Pricing Options Lecture 4: Pricing In Discrete Time Models

This pricing options lecture covers pricing in discrete time models.

1  Discrete time models

 

 

2  Risk-neutral pricing

 

 

3  Fundamental theorem of asset pricing

 

 

4  Binomial tree pricing

 

 

5  Lecture Slides

Download here

 

Course Posts:

Pricing Options Lecture 3: No-arbitrage Pricing Relations

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

1  Model independent relations: forwards, futures, and swaps

 

 

2  Model independent relations: options

 

 

3  Lecture Slides

Download here

 

Course Posts:

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 \omega=\omega_1\omega_2\omega_3\cdots be a successive outcomes of the fair coin toss experiment (\mathbb{P}(H)=\mathbb{P}(T)=\frac{1}{2}). Let’s define a random variable

    \[X_j=\left\{\begin{tabular}{ll}1 & \text{if }\omega_j=H\\ -1?& \text{if }\omega_j=T\\ \end{tabular} \right.\]

and define M_0=0, then we can construct following process M_k,k=0,1,2,\cdots, which is called a symmetric random walk.

    \[M_k=\sum^k_{j=1}X_j,\,k=1,2,\cdots\]

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

Read more Stochastic Calculus Notes 3: Brownian Motion

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 \Omega as the set of all possible outcomes, and denote \omega as one particular outcome.
  • Suppose we are given some information. Such information is not enough to tell the exact value of \omega, 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 \omega 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, \mathcal{F}_0,\mathcal{F}_1,\mathcal{F}_2,\cdots, indexed by time. As time moves forward, we obtain finer resolution, meaning that \mathcal{F}_{t_2} contains more information than \mathcal{F}_{t_1} for any t_1<t_2.
  • Above collection of σ-algebra, \mathcal{F}_0,\mathcal{F}_1,\mathcal{F}_2,\cdots, 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.

1  Pricing deterministic payoffs

 

 

2  Bonds

 

 

3  Lecture Slides

Download here

 

Course Posts:

Pricing Options Lecture 1: Stocks, Bonds, Derivatives

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

1  Welcome

 

 

2  Overview

 

 

3  Stocks, bonds, forwards

 

4  Swaps

 

 

5  Call and put options

 

 

6  Options combinations

 

 

7  Lecture Slides

Download here

 

Course Posts:

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.

 

3  Univariate Random Variables (20:11)

 

4  Cumulative Distribution Function (8:42)

 

5  Quantiles (7:50)

 

6  Standard Normal Distribution (16:02)

 

7  Expected Value and Standard Deviation (19:58)

 

8  General Normal Distribution (6:23)

 

9  Standard Deviation as a Measure of Risk (4:34)

 

10  Normal Distribution: Appropriate for simple returns? (14:22)

 

11  Skewness and Kurtosis (15:39)

 

12  Student’s-t Distribution (5:52)

 

13  Linear Functions of Random Variables (11:13)

 

14  Value at Risk (19:48)

 

15  Introduction-2 (1:04)

 

16  Location-scale Model (12:15)

 

17  Bivariate Discrete Distributions (14:18)

 

18  Bivariate Continuous Distributions (14:15)

 

19  Covariance (19:16)

 

20  Correlation and the Bivariate Normal Distribution (11:59)

 

21  Linear Combination of 2 Random Variables (11:09)

 

22  Portfolio Example (19:20)

 

Course Posts