November 16, 2010MATH 2510: Fin. Math. 2 1 Hand-Outs, I Graded Course Works #2 (brown folder.) Nice work; more comments on Thursday. Course Work #3. Due.

Slides:

Advertisements

Similar presentations

The Normal Distribution

Advertisements

Evaluating Classifiers

Copyright © 2010, 2007, 2004 Pearson Education, Inc. Chapter 18 Sampling Distribution Models.

Copyright © 2010, 2007, 2004 Pearson Education, Inc. Chapter 18 Sampling Distribution Models.

Stochastic Modeling & Simulation Lecture 17 : Probabilistic Inventory Models part 2.

Outline/Coverage Terms for reference Introduction

Copyright © 2010 Pearson Education, Inc. Chapter 18 Sampling Distribution Models.

FE-W EMBAF Zvi Wiener Financial Engineering.

Statistical Significance What is Statistical Significance? What is Statistical Significance? How Do We Know Whether a Result is Statistically Significant?

FE-W EMBAF Zvi Wiener Financial Engineering.

November 30, 2010MATH 2510: Fin. Math. 2 1 Hand-out/in Graded Course Works #3 These slides Repeat appearences Hull’s Chapter 7 on swaps Mock Exam #1.

October 21, 2010MATH 2510: Fin. Math. 2 1 Agenda A lot of hand-outs Comments to Course Work #1 The put-call parity (Hull Ch. 9, Sec. 4) Duration (CT1,

QA-2 FRM-GARP Sep-2001 Zvi Wiener Quantitative Analysis 2.

Statistical Significance What is Statistical Significance? How Do We Know Whether a Result is Statistically Significant? How Do We Know Whether a Result.

Time Series Basics Fin250f: Lecture 3.1 Fall 2005 Reading: Taylor, chapter

Copyright © 2009 Pearson Education, Inc. Chapter 16 Random Variables.

Standard Normal Distribution

November 18, 2010MATH 2510: Fin. Math. 2 1 Hand-Outs, I Hull’s Chapters 2, 3 and 5. Futures markets. Next week’s topic. (Two-word version: think forward.)

Evaluating Classifiers Lecture 2 Instructor: Max Welling.

Simple Linear Regression Statistics 700 Week of November 27.

TODAY Homework 4 comments Week in review -Joint Distribution -Binomial Distribution -Central Limit Theorem Sample problems.

The moment generating function of random variable X is given by Moment generating function.

Need to know in order to do the normal dist problems How to calculate Z How to read a probability from the table, knowing Z **** how to convert table values.

October 28, 2010MATH 2510: Fin. Math. 2 1 Agenda Recap: - A useful duration formula (CT1, Unit 13, Sec. 5.3) - Redington immunisation conditions (CT1,

Estimation and Hypothesis Testing. The Investment Decision What would you like to know? What will be the return on my investment? Not possible PDF for.

Slide 23-1 Copyright © 2004 Pearson Education, Inc.

The Poisson Process. A stochastic process { N ( t ), t ≥ 0} is said to be a counting process if N ( t ) represents the total number of “events” that occur.

Statistics: Examples and Exercises Fall 2010 Module 1 Day 7.

The Binomial Distribution © Christine Crisp “Teach A Level Maths” Statistics 1.

Chapter 6 Lecture 3 Sections: 6.4 – 6.5.

Black Scholes Option Pricing Model Finance (Derivative Securities) 312 Tuesday, 10 October 2006 Readings: Chapter 12.

Stat 13, Tue 5/15/ Hand in HW5 2. Review list. 3. Assumptions and CLT again. 4. Examples. Hand in Hw5. Midterm 2 is Thur, 5/17. Hw6 is due Thu, 5/24.

Copyright © 2009 Pearson Education, Inc. Chapter 18 Sampling Distribution Models.

1 Chapter 18 Sampling Distribution Models. 2 Suppose we had a barrel of jelly beans … this barrel has 75% red jelly beans and 25% blue jelly beans.

More Continuous Distributions

Chapter 5.6 From DeGroot & Schervish. Uniform Distribution.

Finding  and/or  if one/two probabilities are known 50 marks is the pass mark20% of students fail 85 marks is a grade A5% of students get A‘s P(Z

Statistics Workshop Tutorial 5 Sampling Distribution The Central Limit Theorem.

Section 6-5 The Central Limit Theorem. THE CENTRAL LIMIT THEOREM Given: 1.The random variable x has a distribution (which may or may not be normal) with.

Sullivan – Fundamentals of Statistics – 2 nd Edition – Chapter 7 Section 4 – Slide 1 of 11 Chapter 7 Section 4 Assessing Normality.

LECTURE 25 THURSDAY, 19 NOVEMBER STA291 Fall

FIN 614: Financial Management Larry Schrenk, Instructor.

A life insurance company sells a term insurance policy to a 21-year-old male that pays $100,000 if the insured dies within the next 5 years. The probability.

Random Variables (1) A random variable (also known as a stochastic variable), x, is a quantity such as strength, size, or weight, that depends upon a.

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)

The Lognormal Distribution

13.1 Valuing Stock Options : The Black-Scholes-Merton Model Chapter 13.

Valuing Stock Options:The Black-Scholes Model

Chapter 6 Lecture 3 Sections: 6.4 – 6.5. Sampling Distributions and Estimators What we want to do is find out the sampling distribution of a statistic.

TM 661Risk AnalysisSolutions 1 The officers of a resort country club are thinking of constructing an additional 18-hole golf course. Because of the northerly.

1 1 Slide Continuous Probability Distributions n The Uniform Distribution  a b   n The Normal Distribution n The Exponential Distribution.

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:

7.2 Means & Variances of Random Variables AP Statistics.

Chebyshev’s Inequality Markov’s Inequality Proposition 2.1.

Copyright © 2010, 2007, 2004 Pearson Education, Inc. Chapter 18 Sampling Distribution Models.

Sums of Random Variables and Long-Term Averages Sums of R.V. ‘s S n = X 1 + X X n of course.

Final Exam Information These slides and more detailed information will be posted on the webpage later…

Finding the Normal Mean and Variance © Christine Crisp “Teach A Level Maths” Statistics 1.

Cumulative Distribution Function

Continuous Random Variables

Reading a Normal Curve Table

“Teach A Level Maths” Statistics 1

Sample Mean Distributions

Random Variates 2 M. Overstreet Spring 2005

Multiplication Properties

The Normal Probability Distribution Summary

3.3 Experimental Standard Deviation

“Teach A Level Maths” Statistics 1

Central Limit Theorem: Sampling Distribution.

Monday, Nov. 7th 3rd & 6th Please have 2 sharpened pencils, a blank piece of paper, your.

Presentation transcript:

November 16, 2010MATH 2510: Fin. Math. 2 1 Hand-Outs, I Graded Course Works #2 (brown folder.) Nice work; more comments on Thursday. Course Work #3. Due (next) Thursday November 25 (green.) Student surveys; yellow. Fill out and give to me or Maths Taught Student Office. Attendence sheet (just the one.)

November 16, 2010MATH 2510: Fin. Math. 2 2 Hand-Outs, II Updated course plan (blue as usual.) Exercises for Thursday Nov. 17 Workshops. (Qs and As.) Commented table of the normal distribution. These slides. A few spares of CT1, Unit 14 w/ comments. Many spares of last week’s Workshop sol’ns.

November 16, 2010MATH 2510: Fin. Math. 2 3 CT1 Unit 14: Stochastic rates of return Rate of return each period, i t, is stochastic (or: random.) Returns are independent (actually not the worst assumption ever made.) We invest over the horizon 0 to n. What can we say about our time-n wealth? (Expected value, standard deviation, moments, distribution, …)

November 16, 2010MATH 2510: Fin. Math. 2 4 A single (£1) investment The central point of attack is the equation By raising it to powers (1 and 2 mostly; 3 and 4 in CW #3) and taking expectations we arrive at equations for moments in terms of i t -moments. (Nice w/ iid, manageble even if not.)

November 16, 2010MATH 2510: Fin. Math. 2 5 (£1) Annuity investment The central point of attack is the equation By raising it to powers (1 and 2 in particular) and taking expectations we arrive at recursive equations for moments.

November 16, 2010MATH 2510: Fin. Math. 2 6 Annuities w/ the iid returns In case of identically distributed returns we get with j = E(i) and v =´1/(1+j).

November 16, 2010MATH 2510: Fin. Math nd moment of annuity wealth For the second moment we get This is easy the implement in e.g. Excel. (Go to file w/ Table ) (For non-identical i-distributions just put time-indices on j and s.)

November 16, 2010MATH 2510: Fin. Math. 2 8 Log-normal returns Another often used, none-too-bad assumption is A sum of independent, normally distributed random variables is itself normally distributed, and the central point of attack is

November 16, 2010MATH 2510: Fin. Math. 2 9 For single investment we can (when equipped w/ a table of the normal distribution function) find probabilities (for e.g. shortfall or outperformance) easily. A fact: For annuities the (log)normality assumption doesn’t really help much.