Steen Koekebakker

Forward curve dynamics in the Nordic electricity market

The forward curve dynamics in the Nordic electricity market is examined. Six years of price data on futures and forward contracts traded in the Nordic electricity market are analysed. For the forward price function of electricity, we specify a multi‐factor term structure models in a Heath‐Jarrow‐Morton framework. Principal component analysis is used to reveal the volatility structure in the market. A two‐factor model explains 75 per cent of the price variation in our data, compared to approximately 95 per cent in most other markets. Further investigations show that correlation between short‐ and long‐term forward prices is lower than in other markets. We briefly discuss possible reasons why these special properties occur, and some consequences for hedging exposures in this market.

Portfolio Performance Evaluation with Generalized Sharpe Ratios: Beyond the Mean and Variance

This paper presents a theoretically sound portfolio performance measure that takes into account higher moments of distribution. This measure is motivated by a study of the investors preferences to higher moments of distribution within Expected Utility Theory and an approximation analysis of the optimal capital allocation problem. We show that this performance measure justifies the notion of the Generalized Sharpe Ratio (GSR) introduced by Hodges (1998). We present two methods of practical estimation of the GSR: nonparametric and parametric. For the implementation of the parametric method we derive a closed-form solution for the GSR where the higher moments are calibrated to the normal inverse Gaussian distribution. We illustrate how the GSR can mitigate the shortcomings of the Sharpe ratio in resolution of Sharpe ratio paradoxes and reveal the real performance of portfolios with manipulated Sharpe ratios. We also demonstrate the use of this measure in the performance evaluation of hedge funds.

MODELLING FORWARD FREIGHT RATE DYNAMICS -- EMPIRICAL EVIDENCE FROM TIME CHARTER RATES

The purpose of this paper is to investigate the dynamics of forward freight rate dynamics. We specify our model in a Heath–Jarrow–Morton framework. This model was originally developed for interest rate markets and, in subsequent work, the model has been applied to various commodity markets. We analyse ten years of weekly time charter (TC) rates for a Panamax 65,000 dwt bulk carrier. Our data set consists of 6-, 12- and 36-month TC rates. We use this data to construct, each day, a forward rate function using a smoothing algorithm. We use the smooth data to investigate the factors governing the dynamics of the forward freight rate curve. We find a strange volatility structure in the data. Out results show that the volatility of the forward curve is bumped, with volatility reaching a peak for freight rates with roughly one year to maturity. Also, correlations between different parts of the term structure are in general low and even negative.The purpose of this paper is to investigate the dynamics of forward freight rate dynamics. We specify our model in a Heath--Jarrow--Morton framework. This model was originally developed for interest rate markets and, in subsequent work, the model has been applied to various commodity markets. We analyse ten years of weekly time charter ( TC ) rates for a Panamax 65,000 dwt bulk carrier. Our data set consists of 6-, 12- and 36-month TC rates. We use this data to construct, each day, a forward rate function using a smoothing algorithm. We use the smooth data to investigate the factors governing the dynamics of the forward freight rate curve. We find a strange volatility structure in the data. Out results show that the volatility of the forward curve is bumped, with volatility reaching a peak for freight rates with roughly one year to maturity. Also, correlations between different parts of the term structure are in general low and even negative.

Value based trading of real assets in shipping under stochastic freight rates

The article uses a real options valuation model with stochastic freight rates to investigate market efficiency and the economics of switching between the dry bulk and the tanker markets in international shipping. A dry bulk carrier is replaced with a tanker when the expected net present value of such a switch is optimal from a real options based decision rule. Depending on the development of the markets a reversal may take place later. The cost and demand parameters upon which the decisions to switch are made, including the stochastic characteristics of freight rates, are estimated from an empirical analysis that is updated every week throughout a 12-year time period from 1993 to 2005. The second-hand market for bulk ships seems to have been efficient most of these years in the sense that market switching usually did not pay off, with one major exception: it seemed profitable in expectation to leave the dry bulk market and enter the tanker market over a significant period of time shortly after the millennium shift, and to return to the dry bulk market about three years later. These points in time corresponded with an unprecedented boom period in the tanker and dry bulk freight markets, respectively, and the result suggest that agents in the second-hand market were slow to adjust their expectations. In retrospect, such an investment policy also happened to be profitable compared to staying put in the tanker market, even after accounting for transaction costs.

THE CARMA INTEREST RATE MODEL

In this paper, we present a multi-factor continuous-time autoregressive moving-average (CARMA) model for the short and forward interest rates. This model is able to present an adequate statistical description of the short and forward rate dynamics. We show that this is a tractable term structure model and provides closed-form solutions to bond prices, yields, bond option prices, and the term structure of forward rate volatility. We demonstrate the capabilities of our model by calibrating it to a panel of spot rates and the empirical volatility of forward rates simultaneously, making the model consistent with both the spot rate dynamics and forward rate volatility structure.

A Continuous Time Model for Interest Rate with Autoregressive and Moving Average Components

In this paper we present a multi‐factor continuous‐time autoregressive moving‐average (CARMA) model for the short and forward interest rates. This models is able to present a more adequate statistical description of the short and forward rate dynamics. We show that this is a tractable term structure model and provide closed‐form solutions to bond and bond option prices, bond yields, and the forward rate volatility term structure. We demonstrate the capabilities of our model by calibrating it to market data and show that it can reproduce rather complex shapes of the empirical volatility term structure. In particular, a three‐factor CARMA model can easily capture the dynamics of the level, slope, and curvature factors widely documented in term structure models.

Multivariate Modeling and Analysis of Regional Ocean Freight Rates

In this paper, we propose a new multivariate model for the dynamics of regional ocean freight rates. We show that a cointegrated system of regional spot freight rates can be decomposed into a common non-stationary market factor and stationary regional deviations. The resulting integrated CAR process is new to the literature. By interpreting the common market factor as the global arithmetic average of the regional rates, both the market factor and the regional deviations are observable which simplifies the calibration of the model. Moreover, forward contracts on the market factor can be traded in the Forward Freight Agreement (FFA) market. We calibrate the model to historical spot rate processes and illustrate the term structures of volatility and correlation between the regional prices and the market factor. Our model is an important contribution towards improved modelling and hedging of regional price risk when derivative market liquidity is concentrated in a single global benchmark.

Book Review: Derivatives and Risk Management in Shipping by Manolis D. Kavussanos and Ilias D. Visvikis

Derivatives and Risk Management in Shipping, by Manolis D. Kavussanos and Ilias D. Visvikis. Witherbys Publishing, 2006. 392pp. 10-ISBN: 1 85609 310 7; 13-ISBN: 978 1 85609 310 1

Constructing Smooth Forward Curves in Electricity Markets

The intention of this essay is to give a mathematical framework for the construction of maximum smooth forward curves and its application to real market data. In addition to an introductory presentation of the motivation for the need of smooth forward curves and the typical characteristics of commodity markets, basics of risk-neutral forward and swap price modelling are depicted. After introducing the main assumption of the decomposition of the forward curve into a seasonal and an adjustment function, which is proposed by [Benth2008], we give a maximum smoothness criterion which results into a fourth order polynomial spline. Including various constraints (connectivity of spline function resp. its first two derivatives and the observed market prices) we formulate an unconstrained optimization problem using a Lagrange multiplier. Finally, we apply the proposed framework and algorithm to two examples of real electricity market data.