As discussed in section 4.6, the model is solved forwards using value iteration. The exogenous parameters are:
Xexog =
n(xjt), n(yi), Wx(xj,t+1, 0), ˜s(xjt, yi, 0), s(xjt, ∅y, 0), s(∅x, yi, 0), βx, βy, λ
(4.39) where time 0 represents input from outside the model for the first time step.
The endogenous parameters (model outputs) are:
Xendog =
Wx(xjt, t), Wy(yi, t), m(xjt, yi, t)
4.8. Summary 77 where m(xjt, yi, t) is the vector of the assignment in period t.
The dynamic model is solved in the following steps: 1. Step 1. Initialization: set t = 1, set max t = 1000
(a) Input: n(xjt), n(yi); Wx(xj,t+1, 0), s(xjt, ∅y, 0), s(∅x, yi, 0)
(b) Solve the LP problem.
(c) Save outputs Wx(xjt, 1), Wy(yi, 1).
2. Step 2. Set t = 2
(a) Input n(xjt), n(yi); set Wx(xj,t+1, t + 1) = (1 − λ)Wx(xjt, 0) + λWx(xjt, 1);
use Wy(yi, 1) as input to s(∅x, yi, 2).
(b) Solve LP problem.
(c) Check convergence: if |Wx(xjt, t) − Wx(xjt, t − 1)| < and |Wy(yi, t) −
Wy(yi, t − 1)| < then stop.
3. Step 3. For t > 2
(a) Input n(xjt), n(yi); Set Wx(xj,t+1, t + 1) = (1 − λ)Wx(xjt, t − 2) + λWx(xjt, t −
1); Set Wy(yi, t) = (1 − λ)Wy(yi, t − 2) + λWy(yi, t − 1).
(b) Solve LP problem.
(c) Check convergence: if |Wx(xjt, t) − Wx(xjt, t − 1)| < and |Wy(yi, t) −
Wy(yi, t − 1)| < then stop. Else go to Step 3.
4.8
Summary
In this chapter, I have described the matching model structure which will be used to compute the assignment of ships to traders and the earnings for each agent in a competitive equilib- rium. The model is solved using linear programming which is a simple but large combinatorial optimization problem where the combinations are the surpluses from the pairings of agents, including dummy agents. The objective function is to maximize these surpluses subject to the agent constraints which place restrictions on both the number of resources that can be used to fulfill cargo demands and the value each agent must earn (the dummy surplus values for each agent). Associated with solving a linear programming problem are the multipliers on the con- straints which indicate how valuable each type of agent is in the market. The multipliers can be used to construct equilibrium prices. One of the assumptions of the model structure was that the cost of repositioning to the load area is included in the contract price. An alternative
would be for the ship to pay this cost. Either formulation does not have a significant impact on the matching results in the competitive equilibrium however. The model has been divided into two parts: a static one period matching model and a dynamic matching model. The static model uses an estimate of ship option values and dummy surplus values from data outside the model, while these values are determined endogenously in the dynamic version. The purpose of the dynamic model is to solve for a fixed point to see if earnings and matching probabilities converge, keeping the supply and demand stationary.
Chapter 5
Data and Descriptive Statistics
This chapter describes the datasets used to estimate the model described in Chapter 4. Specifi- cally, data on the trade demand between the load and discharge areas by VLCC (the trade flow), the buy price of oil, the expected price of oil in the discharge location, the average cargo size and discount rate is required to estimate the number of trader types and their cargo demands. To estimate the number and types of ships, data is required on the supply of VLCCs in each discharge and waiting area, the technical specifications of the VLCC fleet (age, tonnes per day, design speed, and DWT), and the daily opportunity cost (or rental rate) of the ship. For the matching surplus and the surplus to remain unmatched, data on the pairwise distance of all locations, the bunker price, average operating speed, days in port, per barrel storage cost, and estimated per-tonne freight rates on specific routes is needed.
Data on oil shipments is extremely valuable data. The OPEC countries have a self interest in hiding actual production figures in order to renege against their cartel quota and physical oil traders use shipment information to inform their trading decisions (Downey, 2009). It is difficult to obtain publicly available data from one source that provides complete information on the oil shipment trade flows carried by VLCCs and the prices of fixtures. This chapter describes the five datasets used to estimate the model and documents where there is missing or censored data that presents a challenge for estimation.
The first dataset consists of a sample of world tanker fixtures of crude oil containing price and volume information on trade flows, where a trade flow in the model is defined as total crude oil shipped from load area a to discharge area b. The second dataset contains data on benchmark prices for trade flows which are used to compute prices. The third dataset provides data on the VLCC fleet which is used to create physical profiles of ships. The fourth dataset is a compilation of aggregate trade data used to compute the implied average number of ships in each area. The fifth dataset provides ship movement characteristics including speed travelled.
5.1
Fixtures dataset
The fixtures dataset (Clarkson Research, 2011) is a sample of global crude oil tanker voyage (spot) and time charter contracts for the time period between January 2, 2007 to December 13, 2011. The data contains 39,022 observations grouped into fixture contract details relating to the shipowner and charterer. Clarkson Research reports the deals for which shipping brokers are willing to record; some are withheld from the market for confidential reasons (Cridland, 2010). According to Clarkson Research (2011), “Charter rates for specific fixtures are often omitted when reported to the market for a variety of reasons. For example, it may just not have been available when the various brokering houses/the Baltic Exchange reported the fixture. However, it is safe to assume that on the whole, if the rate is not available, it is more likely than not to be for confidentiality reasons.” According to the sources, between 2007-2011, approximately 8,000 fixtures or 20% were marked private and confidential and were excluded from the dataset. The dataset contains detailed information on the fixture, fleet detail, and origin and destination. The fixture detail includes the fixture date, freight rate, laycan from and to, fixture status, charterer name, beneficial shipowner, and origin and destination information. Laycan from and to refers to the earliest and latest dates when the ship can load, respectively. There is various geographical coverage, with some entries reporting detail to the port level. Rates either reported in Worldscale (WS), lump sum, US dollars per day (for time charter contracts), or are not reported at all (reported as 0). I refer to fixtures with prices that are not reported as censored fixtures, while fixtures that were excluded from the dataset by the data source are omitted fixtures.
The majority of observations for the voyage contracts are reported in WS units and occa- sionally quoted in lump sum units depending on the source of the information and the specifics of the charter party. The lump sum is the gross revenue per voyage.
Fleet register detail on the ship’s physical characteristics includes the vessel name, IMO number, builder, builder country, flag state, main engine manufacturer, vessel design speed, vessel daily fuel consumption, and total engine propulsion (horsepower). Table 5.1 shows there are 9 types of vessels included: Aframax, Capesize, FPSO/FSU, Handy, Offshore, Panamax, Suezmax, and VLCC. VLCCs account for the largest volume of tonnes lifted (52%) of all vessel classes. The subset of VLCC fixtures contains 4,873 observations and the remaining discussion of the fixtures dataset will focus on this subset.
5.1. Fixtures dataset 81 Table 5.1: Cargo volume by vessel type, 2007-2011
Vessel Cargo Volume Share of Volume
’000 tonnes % VLCC 1,139,826 51.9 Aframax 506,407 23.1 Suezmax 328,447 15.0 Capesize 120,202 5.5 FPSO/FSU 79,673 3.6 Panamax 9,810 0.4 Offshore 5,022 0.2 Combined 4,720 0.2
Source: Clarkson Research (2011)