Seasonality in cocoa spot and forward markets: empirical evidence

This paper first describes the main features of supply and demand in cocoa spot markets. A state- variable model is proposed to describe the random evolution of cocoa forward curves over time, which essentially adapts to agricultural commodities, introduced by Borovkova and Geman (2006) for energy. In contrast to most of the literature on the subject, the first state variable is not the spot price, as it combines seasonal and stochastic features and may not be observable, instead, the average value of all liquid futures contracts is a quantity devoid of seasonality and conveys a robust representation of the forward curve level. The second state variable is a quantity analogous to the stochastic convenience yield, which accounts for the random changes in the shape of the forward curve. We conduct estimation procedures for the cocoa market over the period of 1980 to 2009 and exhibit an interesting result on cocoa seasonality as well as an extension of the Samuelson effect

Understanding the fine structure of electricity prices

This paper analyzes the special features of electricity spot prices derived from the physics of this commodity and from the economics of supply and demand in a market pool. Besides mean reversion, a property they share with other commodities, power prices exhibit the unique feature of spikes in trajectories. We introduce a class of discontinuous processes exhibiting a "jump-reversion" component to properly represent these sharp upward moves shortly followed by drops of similar magnitude. Our approach allows to capture—for the first time to our knowledge—both the trajectorial and the statistical properties of electricity pool prices. The quality of the fitting is illustrated on a database of major U.S. power markets

Shipping markets and freight rates: an analysis of the Baltic Dry Index

Shipping, although a crucial component of the transportation of commodities worldwide, is hardly present in the finance literature at this point. The first and foremost goal of this paper is to describe and explain from an economic perspective the key features of shipping markets; the second one is to analyze the behavior of freight rates, which define the final cost of an imported commodity. We focus on the major index, the BDI (Baltic Dry Index) and propose some diffusion models able to capture the unique features of its trajectories, namely large swings and continuity. Their performance is exhibited on a database covering the period 1988-2010. Such spot models should facilitate the growth of the market of freight rates options, a safe hedging instrument for farmers and cooperatives that ship their grains to distant destinations

Understanding the Fine Structure of Electricity Prices.

This paper analyzes the special features of electricity spot prices derived from the physics of this commodity and from the economics of supply and demand in a market pool. Besides mean-reversion, a property they share with other commodities, power prices exhibit the unique feature of spikes in trajectories. We introduce a class of discontinuous processes exhibiting a jump-reversion component to properly represent these sharp upward moves shortly followed by drops of similar magnitude. Our approach allows to capture - for the first time to our knowledge - both the trajectorial and the statistical properties of electricity pool prices. The quality of the fitting is illustrated on a database of major US power markets.Energy price risk; Simulation; Calibration; Statistical estimations; Jump diffusions; Electricity prices;

Fertilizers markets: in search of the index of choice

The goal of the paper is twofold: i) Re-examine the different definitions that ‘financialization’ has conveyed in the large recent literature on commodities; ii) argue in favour of visible indexes in the creation of reliable derivatives markets, taking the remarkable example of the Liquid Natural Gas indexes and inferring some lessons for the creation of derivatives in fertilizer market

Options on Hedge Funds under the High Water Mark Rule

The rapidly growing hedge fund industry has provided individual and institutional investors with new investment vehicles and styles of management. It has also brought forward a new form of performance contract: hedge fund managers receive incentive fees which are typically a fraction of the fund net asset value (NAV) above its starting level - a rule known as high water mark. Options on hedge funds are becoming increasingly popular, in particular because they allow investors with limited capital to get exposure to this new asset class. The goal of the paper is to propose a valuation of plain-vanilla options on hedge funds which accounts for the high water market rule. Mathematically, this valuation leads to an interesting use of local times of Brownian motion. Option prices are numerically computed by inversion of their Laplace transforms

On pricing risky loans and collateralized fund obligations

Loan spreads are analyzed for two types of loans. The first type takes losses at maturity only; the second follows the formulation of collateralized fund obligations, with losses registered over the lifetime of the contract. In both cases, the implementation requires the choice of a process for the underlying asset value and the identification of the parameters. The parameters of the process are inferred from the option volatility surface by treating equity options as compound options with equity itself being viewed as an option on the asset value with a strike set at the debt level following Merton. Using data on the stock of General Motors during 2002-3, we show that the use of spectrally negative Lévy processes is capable of delivering realistic spreads without inflating debt levels, deflating debt maturities or deviating from the estimated probability laws

Valuation of default sensitive claims under imperfect information.

We propose an evaluation method for financial assets subject to default risk, when investors face imperfect information about the state variable triggering the default. The model we propose generalizes the one by Duffie and Lando (2001) in the following way:(i)it incorporates informational noise in continuous time, (ii) it respects the (H) hypothesis, (iii) it precludes arbitrage from insiders. The model is sufficiently general to encompass a large class of structural models. In this setting we show that the default time is totally inaccessible in the market’s filtration and derive the martingale hazard process. Finally, we provide pricing formulas for default-sensitive claims and illustrate with particular examples the shapes of the credit spreads and the conditional default probabilities. An important feature of the conditional default probabilities is they are non Markovian. This might shed some light on observed phenomena such as the ”rating momentum”.hybrid models; default sensitive claims;

Revisiting uncertainty and price forecast indicators in corn and wheat markets

The purpose of this paper is twofold: First, we look at the fundamentals of spot prices of corn and wheat and analyse several measures of dispersion, arguing that the use of the standard deviation of prices is more instructive for regulators and world food organisations than volatility, that is, standard deviation of returns. Second, we look at alternative predictors of corn and wheat spot prices and exhibit that the average value of the forward curve introduced by Borovkova and Geman (2006) performs better than individual forward prices to forecast spot prices at future dates

Spot price modelling of industrial metals – an heterogeneous agent based model for Copper

Abstract We will show in this paper the role of inventories in explaining copper price volatility. Using a three factor model we derive a fundamental long-term value for copper. Second, we emphasis the significance of this fundamental long-term value by considering an agent based model approach in which mean-reversion focused fundamental investors trade with chartists who follow price trends. We show that fundamental investors take increasing positions in copper when the spot price of copper deviated from its fundamental value (i.e. the fundamental value is higher than the spot price) and chartists loose relative significance