Cuadernos del CIPE No. 40. The Ornstein - Uhlenbeck process. An introduction for commodity modelling with smeextensions.

An example for the London Cocoa Net Spot Convenience Yield

- Autor: Carlos Armando Mejía Vega

Descripción›

One of the canonical models for commodity international financial markets is known as the Gibson and Schwartz (1990) model. In this model, a second variable different from the Standard Spot Price of the commodity, known as the Net Spot Convenience Yield, is modelled through an Ornstein-Uhlenbeck process. Based on this, it is fundamental for anyone who aims to work in the commodity modelling field to know the particularities of this stochastic process: (I) its general history; (II) the intuition and interpretation behind it; (III) its general solution; (IV) so me of its particular characteristics; (V) the statistics inspired by it that help to test the presence of a mean-reverting pattern or not of a time-series and (VI) the calibration methods. Finally, so me of these features will be applied to the concrete case of the London Cocoa Net Spot Convenience Yield.

Tipo de Contenido›

Prologue

Introduction

Chapter 1. General history

Chapter 2. The stochastic process

2.1 Solution part I. Intuition as a deterministic process

2.2 Solution part II. Definition of the dependent process and partial derivatives

2.3 Solution part III, ItO´s lemma application

2.4 Solution part IV. Integration from s to t, where 0 = s < t

2.5 Gaussian property

2.6 Solution part VI. Discretization process

2.7 Stationary property

2.7.1 Constant long - term Expected Value

2.7.2 Constant long-term Variance

2.7.3 Covariance

Chapter 3. The Dickey - Fuller test

3.1 Testing the mean-reverting pattern of a time series

3.2 The Dickey Fuller test with and without drift

Chapter 4. Calibration prócess

4.1 Maximum Log-Likelihood Method

4.1.1 Log-Likelihood function

4.1.2 First order conditions

4.1.3 Final equations

4.1.4 Particular issues about the parameters

4.2 Regression method

4.2.1 Regression model

4.2.2 Least Square Regression Method

4.3.3 Final equations

Chapter 5. Example for the London Cocoa Net Spot Convenience Yield

5.1 The class of futures contracts over commodities known as the London Cocoa Futures

5.2 Proxy for the London Cocoa Net Spot Convenience Yield

5.3 Mean reversion pattern

5.4 Parameters calibration

Bibliography

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Cuadernos del CIPE No. 40. The Ornstein - Uhlenbeck process. An introduction for commodity modelling with smeextensions.

An example for the London Cocoa Net Spot Convenience Yield

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