A Valuation of Options to Extend the Time Charter Period: The Application of Artificial Neural Networks

Options in the shipping market consist of paper freight options and physicaloptions attached to charterparties or newbuilding contracts. The options most frequently associated with the physical shipping market are options to extend the charter period on time charters and additional shipment options attached to contracts of affreightment. In both the paper market and the physical market, the value of freight options, in practice, is estimated mostly by referring to the forward curves of freight derivatives. The option on freight has different properties from its financial counterparts, and the straightforward adoption of theoretical models like the Black-Sholes option pricing model (BSM) has not produced promising results. So far, academic research in this field has also hardly made a meaningful contribution to practice and is in need of further elaboration. This research focuses on the period extension options attached to time charter contracts. In this paper, extension options, which have the property of options on futures, were conceptually transformed into regular European call options before the BSM was applied. The efficient market hypothesis (EMH), which justifies the parity of the performance of a long-term charter to that of repetitive short-term charters for the same period, worked as the basis of the conversion. The option values determined by the BSM were compared with the actual realized values to verify the applicability of the model. Additionally, a robust relationship mapping model, artificial neural networks (ANN), was employed to derive the option values, and then the results were compared with those of the BSM. The ANN is recently expanding its application to business, finance, and management, and is drawing attention in the areas of discrimination, pattern recognition, and forecasting. This study is meaningful as the first-time application of both the closed-form solution and the ANN to the valuation of physical freight options. In particular, the application of the ANN is expected to lead the active adoption of machine learning tools in the analysis of shipping market behavior. The result of this research can contribute to enhancing the quality of chartering decisions by providing criteria to determine option values. The decision rationality to be achieved by the model can be contrasted with the fact that, so far, decisions have been made with a ‘rule-ofthumb’ valuation of options. The extension option, in reality, tends to be granted to charterers with better credit, even free of charge when the market is at its trough. Hence, the results could also be used as a tool to quantify counterparty risk. This analysis is limited to the Panamax bulk market, which has long-term data consistency. The extension of the study to other segments of bulk shipping such as Cape, Supramax and even to wet bulk markets will help generalize the model’s performance. The result also implies the ‘forecasting’ performance of the ANN because the value of the extension options contains the information required to make freight market forecasts. Therefore, the study can be extended to the area of forecasting. In that case, the performances can be tested with additional input variables, such as forward market features, to the BSM input variables.List of Tables .................................................................................................................................. vi List of Figures ............................................................................................................................... vii 요 약 ............................................................................................................................................. viii Abstract .............................................................................................................................................. x Chapter 1 Introduction……………………………………………………………..…….1 1.1 Background .............................................................................................................................. 1 1.2 Research Purposes ................................................................................................................ 2 1.3 Research Scope ...................................................................................................................... 3 1.4 Research Procedures ............................................................................................................ 4 1.5 Contribution ............................................................................................................................. 6 1.6 Structure of the Paper ......................................................................................................... 7 Chapter 2 Bulk Shipping and Freight Options…………………………..……….8 2.1 Bulk Shipping as Freight Trading ................................................................................... 8 2.1.1 Freight trading ........................................................................................................ 8 2.1.2 Risk management ................................................................................................ 14 iv 2.2 Freight Options .................................................................................................................... 15 2.2.1 Paper freight options ......................................................................................... 16 2.2.2 Physical freight options .................................................................................... 18 Chapter 3 Literature Review…………………………………………………………..23 3.1 Asian Option Approximation .................................................................................... 23 3.2 Option on Futures ......................................................................................................... 25 3.3 European Options .......................................................................................................... 25 3.3.1 Binomial option pricing model ................................................................... 26 3.3.2 Black-Scholes option pricing model ....................................................... 26 3.4 Efficient Market Hypothesis and Expectations Theory ................................. 27 3.5 Artificial Neural Networks .......................................................................................... 30 Chapter 4 Data and Basic Assumptions…………………………………………..35 4.1 Data ...................................................................................................................................... 35 4.2 Basic Assumptions ......................................................................................................... 37 Chapter 5 Black-Scholes Option Pricing Model………………………………..40 5.1 The BSM ............................................................................................................................. 40 5.2 Input Variables ................................................................................................................. 43 v Chapter 6 Artificial Neural Networks………………………………………………44 6.1 Network Structure .......................................................................................................... 46 6.2 Normalization .................................................................................................................. 51 Chapter 7 Results………………………………………………………………………….53 7.1 Measurements ................................................................................................................. 53 7.2 Black-Scholes Option Pricing Model ..................................................................... 54 7.3 Artificial Neural Networks .......................................................................................... 55 7.4 Comparison ....................................................................................................................... 58 Chapter 8 Conclusion………………………………………………………………..60 References ...................................................................................................................................... 63 Appendix I ...................................................................................................................................... 68 Appendix II .................................................................................................................................... 74Docto

Automatic, computer aided geometric design of free-knot, regression splines

A new algorithm for Computer Aided Geometric Design of least squares (LS) splines with variable knots, named GeDS, is presented. It is based on interpreting functional spline regression as a parametric B-spline curve, and on using the shape preserving property of its control polygon. The GeDS algorithm includes two major stages. For the first stage, an automatic adaptive, knot location algorithm is developed. By adding knots, one at a time, it sequentially "breaks" a straight line segment into pieces in order to construct a linear LS B-spline fit, which captures the "shape" of the data. A stopping rule is applied which avoids both over and under fitting and selects the number of knots for the second stage of GeDS, in which smoother, higher order (quadratic, cubic, etc.) fits are generated. The knots appropriate for the second stage are determined, according to a new knot location method, called the averaging method. It approximately preserves the linear precision property of B-spline curves and allows the attachment of smooth higher order LS B-spline fits to a control polygon, so that the shape of the linear polygon of stage one is followed. The GeDS method produces simultaneously linear, quadratic, cubic (and possibly higher order) spline fits with one and the same number of B-spline regression functions. The GeDS algorithm is very fast, since no deterministic or stochastic knot insertion/deletion and relocation search strategies are involved, neither in the first nor the second stage. Extensive numerical examples are provided, illustrating the performance of GeDS and the quality of the resulting LS spline fits. The GeDS procedure is compared with other existing variable knot spline methods and smoothing techniques, such as SARS, HAS, MDL, AGS methods and is shown to produce models with fewer parameters but with similar goodness of fit characteristics, and visual quality

The History of the Quantitative Methods in Finance Conference Series. 1992-2007

This report charts the history of the Quantitative Methods in Finance (QMF) conference from its beginning in 1993 to the 15th conference in 2007. It lists alphabetically the 1037 speakers who presented at all 15 conferences and the titles of their papers.

The Value of IS-Enabled Flexibility in Electricity Demand - a Real Options Approach

As the transition to renewable energy sources progresses, their integration makes electricity production increasingly fluctuating, also causing amplified volatility in electricity prices on energy markets. To contribute to power grid stability, utilities need to balance volatile supply through shifting demand. This measure of demand side management creates flexibility, being enabled as the integration of IS in the power grid grows. The flexibility of deferring consumption to times of lower demand or higher supply bears an economic value. We show how to quantify this value in order to support decisions on short-term consumer compensation. We adapt real options theory, which has been widely used in IS research for valuation under uncertainty. Addressing a prerequisite, we develop a stochastic process, which realistically replicates intraday electricity spot price development. We employ it in a binomial tree model to assess the value of IS-enabled flexibility in electricity demand

Numerical methods for option pricing.

This thesis aims to introduce some fundamental concepts underlying option valuation theory including implementation of computational tools. In many cases analytical solution for option pricing does not exist, thus the following numerical methods are used: binomial trees, Monte Carlo simulations and finite difference methods. First, an algorithm based on Hull and Wilmott is written for every method. Then these algorithms are improved in different ways. For the binomial tree both speed and memory usage is significantly improved by using only one vector instead of a whole price storing matrix. Computational time in Monte Carlo simulations is reduced by implementing a parallel algorithm (in C) which is capable of improving speed by a factor which equals the number of processors used. Furthermore, MatLab code for Monte Carlo was made faster by vectorizing simulation process. Finally, obtained option values are compared to those obtained with popular finite difference methods, and it is discussed which of the algorithms is more appropriate for which purpose