Non-gaussian behaviour of some commodities prices

Slides:

Advertisements

Similar presentations

Dummy Variables. Introduction Discuss the use of dummy variables in Financial Econometrics. Examine the issue of normality and the use of dummy variables.

Advertisements

Hedging with Black and scholes Analytical Finance I Ellen Bjarnadóttir, Helga Daníelsdóttir and Koorosh Feizi.

Overview of Quantitative Finance and Risk Management Research By Dr. Cheng-Few Lee Distinguished Professor, Rutgers University, USA Distinguished Professor,

Bounding Option Prices Using Semidefinite Programming S ACHIN J AYASWAL Department of Management Sciences University of Waterloo, Canada Project work for.

Change of Time Method in Mathematical Finance Anatoliy Swishchuk Mathematical & Computational Finance Lab Department of Mathematics & Statistics University.

Chapter 2. Unobserved Component models Esther Ruiz PhD Program in Business Administration and Quantitative Analysis Financial Econometrics.

COMM 472: Quantitative Analysis of Financial Decisions

Applications of Stochastic Processes in Asset Price Modeling Preetam D’Souza.

MGT 821/ECON 873 Volatility Smiles & Extension of Models

5/23/2015 Tactical Asset Allocation 1 Tactical Asset Allocation 2 session 6 Andrei Simonov.

Primbs, MS&E 345, Spring The Analysis of Volatility.

Final project: Exploring the structure of correlation Forrest White, Jason Wei Joachim Edery, Kevin Hsu Yoan Hassid MS&E /02/2010.

Time evolution of the probability distribution of returns in the Heston model of stochastic volatility compared with the high-frequency stock-market data.

Empirical Financial Economics 4. Asset pricing and Mean Variance Efficiency Stephen Brown NYU Stern School of Business UNSW PhD Seminar, June

Stochastic Calculus and Model of the Behavior of Stock Prices.

Financial Stylized Facts Fin250f: Lecture 3.3 Fall 2005 Reading: Taylor, chapter 4.

28-Sep-04SS Get Folder Network Neighbourhood –Tcd.ie Ntserver-usr –Get »richmond.

Change of Time Method: Application to Mathematical Finance. I. Anatoliy Swishchuk Math & Comp Finance Lab Dept of Math & Stat, U of C ‘Lunch at the Lab’

JUMP DIFFUSION MODELS Karina Mignone Option Pricing under Jump Diffusion.

Seiji Armstrong Huy Luong Huy Luong Alon Arad Alon Arad Kane Hill Kane Hill.

Fast Fourier Transform for Discrete Asian Options European Finance Management Association Lugano June 2001 Eric Ben-Hamou

A Universal Framework For Pricing Financial and Insurance Risks Presentation at the ASTIN Colloquium July 2001, Washington DC Shaun Wang, FCAS, Ph.D.

Empirical Financial Economics Asset pricing and Mean Variance Efficiency.

Pricing the Convexity Adjustment Eric Benhamou a Wiener Chaos approach.

Realized Volatility Distribution in Japanese Stock Market Tetsuya Takaishi Hiroshima University of Economics To be published in Evolutionary and Institutional.

A 1/n strategy and Markowitz' problem in continuous time Carl Lindberg

Derivation of the Beta Risk Factor

MONTE CARLO SIMULATION. Topics History of Monte Carlo Simulation GBM process How to simulate the Stock Path in Excel, Monte Carlo simulation and VaR.

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.

STABLE NON-GAUSSIAN ASSET ALLOCATION:A COMPARISON WITH THE CLASSICAL GAUSSIAN APPROACH Yesim Tokat, Svetlozar Rachev, and Eduardo Schwartz.

1 4. Empirical distributions & prediction of returns 4.1 Prices and returns Price (P) ACF decays slowly. Log price: p = log(P) Single-period (rate of)

© The MathWorks, Inc. ® ® Monte Carlo Simulations using MATLAB Vincent Leclercq, Application engineer

Option Pricing Models: The Black-Scholes-Merton Model aka Black – Scholes Option Pricing Model (BSOPM)

FMG PH.D. seminar (21 October 1999) slide 1 Dynamic Hedging with Transaction Costs Outline: -Introduction -Adjusted path and Strategy -Leland model and.

Page 1CS March 2002 Value Based Software Reuse Investment A Review Susan K. Donohue Department of Systems and Information Engineering.

Dissertation paper Modelling and Forecasting Volatility Index based on the stochastic volatility models MSc Student: LAVINIA-ROXANA DAVID Supervisor: Professor.

MSc COURSE : ASSET PRICING AND PORTFOLIO THEORY. Aims Introduce basic concepts used to price financial assets Introduce basic concepts used to price financial.

Multifractality. Theory and Evidence An Application to the Romanian Stock Market MSc Student: Cristina-Camelia Paduraru Supervisor: PhD Professor Moisa.

Lecture 3. Option Valuation Methods  Genentech call options have an exercise price of $80 and expire in one year. Case 1 Stock price falls to $60 Option.

13 th AFIR Colloquium 2003 The estimation of Market VaR using Garch models and a heavy tail distributions The dynamic VaR and The Static VaR The Garch.

ARCH AND GARCH V AIBHAV G UPTA MIB, D OC, DSE, DU.

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.

Stochastic Calculus and Model of the Behavior of Stock Prices.

The Generalized extreme value (GEV) distribution, the implied tail index and option pricing Sheri Markose and Amadeo Alentorn Papers available at:

Discussion of Mandelbrot Themes: Alpha (Tail Index) and Scaling (H) Prepared by Sheri Markose, Amadeo Alentorn and Vikentia Provizionatou WEHIA 2005 Implications.

Lecture 8 Stephen G. Hall ARCH and GARCH. REFS A thorough introduction ‘ARCH Models’ Bollerslev T, Engle R F and Nelson D B Handbook of Econometrics vol.

Applications of Stochastic Processes in Asset Price Modeling Preetam D’Souza.

1 VaR Models VaR Models for Energy Commodities Parametric VaR Historical Simulation VaR Monte Carlo VaR VaR based on Volatility Adjusted.

The Black-Scholes-Merton Model

The Three Common Approaches for Calculating Value at Risk

Lec 13a Black & Scholes OPM

The Black-Scholes Model for Option Pricing

Centre of Computational Finance and Economic Agents

Distortion Risk Measures and Economic Capital

Financial Risk Management of Insurance Enterprises

Stochastic Volatility Models: High Frequency Data & Large Volatilities

Alternative Investments and Risk Measurement

Random WALK, BROWNIAN MOTION and SDEs

Baosheng Yuan and Kan Chen

VaR Introduction I: Parametric VaR Tom Mills FinPricing

Detection of financial crisis by methods of multifractal analysis

Brownian Motion & Itô Formula

Forecasting the daily dynamic hedge ratios in agricultural futures markets: evidence from the GARCH models Yuanyuan Zhang, School of Management, University.

Chp.9 Option Pricing When Underlying Stock Returns are Discontinuous

Options valuation Stefano Grazioli.

Options valuation Stefano Grazioli.

Numerical Methods in Finance

FORECASTING VOLATILITY I

Presentation transcript:

Non-gaussian behaviour of some commodities prices José Augusto M. de Andrade Jr Tabajara Pimenta Jr (PhD)

Agenda Introduction Stylized facts Impacts over financial engineering Data and methodology Discussion of empirical results Conclusions

Introduction Pareto law Bachelier(1900) Mandelbrot(1963) & econophysics Black & Scholes options pricing formula Stylized facts

Stylized facts High kurtosis (>3) – heavy tails – Noah effect Volatility clustering Long-term memory (Hurst & Joseph Effect) Scaling

Impacts over financial engineering Options & stocks pricing (B&S formula) Brownian motion – Wiener process S(T) = S(0) exp ( [ r – 1/2 σ 2] T + σW(T) ) CAPM Risk / Return – Covariance / Variance Risk Unconditional distribution Markovitz portfolio optimization model Variance / covariance

Data and methodology Data

Methods Non-parametric tests for normality BDS test for i.i.d. Kolgomorov-Smirnov Chi-square Shapiro-Francia Shapiro-Wilkinson Anderson-Darling BDS test for i.i.d.

Discussion of results

Results

Conclusions The commodities log-returns analysed are not gaussian They are not i.i.d. – so the underlaying process is nonlinear stochastic (non-Gaussian) or deterministic (chaos) The financial engineering tools are based on gaussian assumptions So, these tools cannot give reliable results as they are based on false assumptions

Further research Another distribution – stable paretian models Petrobras paper – the results