Financial Mathematics. In finance, a hedge is an investment that is taken out specifically to reduce or cancel out the risk in another investment.financerisk.

Slides:



Advertisements
Similar presentations
Let X 1, X 2,..., X n be a set of independent random variables having a common distribution, and let E[ X i ] = . then, with probability 1 Strong law.
Advertisements

Distributions of sampling statistics Chapter 6 Sample mean & sample variance.
Week11 Parameter, Statistic and Random Samples A parameter is a number that describes the population. It is a fixed number, but in practice we do not know.
Statistics 1: Introduction to Probability and Statistics Section 3-3.
Some Financial Mathematics. The one-period rate of return of an asset at time t. where p t = the asset price at time t. Note: Also if there was continuous.
Chapter 8 – Normal Probability Distribution A probability distribution in which the random variable is continuous is a continuous probability distribution.
Descriptive statistics Experiment  Data  Sample Statistics Experiment  Data  Sample Statistics Sample mean Sample mean Sample variance Sample variance.
4. Convergence of random variables  Convergence in probability  Convergence in distribution  Convergence in quadratic mean  Properties  The law of.
Standard Normal Distribution
Recruitment
Asset Pricing Theory Option A right to buy (or sell) an underlying asset. Strike price: K Maturity date: T. Price of the underlying asset: S(t)
The moment generating function of random variable X is given by Moment generating function.
Jeff Hosea : University of Surrey, Physics Dept, Level 1 Labs, Oct Level 1 Laboratories A Rough Summary of Key Error Formulae for samples of random.
Section 5.6 Important Theorem in the Text: The Central Limit TheoremTheorem (a) Let X 1, X 2, …, X n be a random sample from a U(–2, 3) distribution.
Today Today: Chapter 8, start Chapter 9 Assignment: Recommended Questions: 9.1, 9.8, 9.20, 9.23, 9.25.
The Central Limit Theorem For simple random samples from any population with finite mean and variance, as n becomes increasingly large, the sampling distribution.
Normal and Sampling Distributions A normal distribution is uniquely determined by its mean, , and variance,  2 The random variable Z = (X-  /  is.
Continuous Probability Distribution  A continuous random variables (RV) has infinitely many possible outcomes  Probability is conveyed for a range of.
Options Pricing and Black-Scholes By Addison Euhus, Guidance by Zsolt Pajor-Gyulai.
Chapter 6 Sampling and Sampling Distributions
Sampling Distributions  A statistic is random in value … it changes from sample to sample.  The probability distribution of a statistic is called a sampling.
Black-Scholes Option Valuation
B AD 6243: Applied Univariate Statistics Understanding Data and Data Distributions Professor Laku Chidambaram Price College of Business University of Oklahoma.
MTH 161: Introduction To Statistics
Measures of Variability Objective: Students should know what a variance and standard deviation are and for what type of data they typically used.
Physics 270 – Experimental Physics. Standard Deviation of the Mean (Standard Error) When we report the average value of n measurements, the uncertainty.
Hedging with Forward & Futures Risk Management Prof. Ali Nejadmalayeri, Dr N a.k.a. “Dr N”
Intermediate Investments F3031 Option Pricing There are two primary methods we will examine to determine how options are priced –Binomial Option Pricing.
Sampling Distribution of the Sample Mean. Example a Let X denote the lifetime of a battery Suppose the distribution of battery battery lifetimes has 
Lab 3b: Distribution of the mean
Week11 Parameter, Statistic and Random Samples A parameter is a number that describes the population. It is a fixed number, but in practice we do not know.
Chapter 7 Sampling and Sampling Distributions ©. Simple Random Sample simple random sample Suppose that we want to select a sample of n objects from a.
Chapter 7: Introduction to Sampling Distributions Section 2: The Central Limit Theorem.
7 sum of RVs. 7-1: variance of Z Find the variance of Z = X+Y by using Var(X), Var(Y), and Cov(X,Y)
B AD 6243: Applied Univariate Statistics Data Distributions and Sampling Professor Laku Chidambaram Price College of Business University of Oklahoma.
Barnett/Ziegler/Byleen Finite Mathematics 11e1 Chapter 11 Review Important Terms, Symbols, Concepts Sect Graphing Data Bar graphs, broken-line graphs,
13.1 Valuing Stock Options : The Black-Scholes-Merton Model Chapter 13.
Topic 5 - Joint distributions and the CLT
1 Sampling distributions The probability distribution of a statistic is called a sampling distribution. : the sampling distribution of the mean.
Chapter 18 Sampling Distribution Models *For Means.
Chapter 5 Joint Probability Distributions and Random Samples  Jointly Distributed Random Variables.2 - Expected Values, Covariance, and Correlation.3.
Paul Cornwell March 31,  Let X 1,…,X n be independent, identically distributed random variables with positive variance. Averages of these variables.
Central Limit Theorem Let X 1, X 2, …, X n be n independent, identically distributed random variables with mean  and standard deviation . For large n:
Chi Square Test for Goodness of Fit Determining if our sample fits the way it should be.
OPTIONS PRICING AND HEDGING WITH GARCH.THE PRICING KERNEL.HULL AND WHITE.THE PLUG-IN ESTIMATOR AND GARCH GAMMA.ENGLE-MUSTAFA – IMPLIED GARCH.DUAN AND EXTENSIONS.ENGLE.
BA 275 Quantitative Business Methods
Geology 6600/7600 Signal Analysis 04 Sep 2014 © A.R. Lowry 2015 Last time: Signal Analysis is a set of tools used to extract information from sequences.
Learning Objectives LO 1: Explain the basic characteristics and terminology of options. LO 2: Determine the intrinsic value of options at expiration date.
Sampling and Sampling Distributions
Ch5.4 Central Limit Theorem
Probability Review for Financial Engineers
Chapter 8: Fundamental Sampling Distributions and Data Descriptions:
Sample Mean Distributions
Project Management Simulation, U-Distribution
Frequency and Distribution
Chapter 7: Sampling Distributions
Mathematical Finance An Introduction
C14: The central limit theorem
01 דצמבר 18.
Lecture 2 – Monte Carlo method in finance
Lecture Slides Elementary Statistics Twelfth Edition
Lecture Slides Elementary Statistics Twelfth Edition
Project Planning Simulation
Sampling Distributions
Vital Statistics Probability and Statistics for Economics and Business
Central Limit Theorem: Sampling Distribution.
Chapter 8: Fundamental Sampling Distributions and Data Descriptions:
Review of Hypothesis Testing
Numerical Methods in Finance
Fundamental Sampling Distributions and Data Descriptions
Presentation transcript:

Financial Mathematics

In finance, a hedge is an investment that is taken out specifically to reduce or cancel out the risk in another investment.financerisk

central limit theorem (CLT) states that the sum of a large number of independent and identically-distributed random variables will be approximately normally distributed (i.e., following a Gaussian distribution, or bell-shaped curve) if the random variables have a finite variance. independent and identically-distributed random variables normally distributedi.e.finite

Call Option Put Option Lets look at some equity option markets D

Black Scholes Pricing Option Formula

Statistical Arbitrage

Pairs Trading Ford and GM

Co-Integration Excel: Simple_Cointegration_Example.xls