Matrics - Use Consistent Forward Curves
Use Consistent Curves Generated in Real Time

Unlike stock markets, forward freight rates normally have complicated term structures. Forward rates may be falling or rising and will often include seasonal effects. Market prices are available on a varying time granularity, typically starting with single months in the front and ending with whole years in the end. These market prices are naturally seen as averages of an underlying continuous forward curve. To be able to price all time periods in a consistent manner, a trading system should work with the underlying forward curve, preferably using a daily granularity. This is particularly important when dealing with physical assets, since these have time periods that seldom correspond to the periods traded in the financial market.

Matrics comes with a state-of-the-art forward curve generator. It can be used immediately with default settings, but also allows extensible customization for organizations that wants to do so. The forward curves are updated immediately when new price info becomes available and are used as basis for real-time pricing of all contracts.

Handle Overlapping Inputs and Identify Arbitrages

The curve generator will quickly construct a smooth curve from any set of forward products. The constructed curve will be maximally smooth in a precise mathematical sense. Furthermore, it will price back all input products used to construct the curve, i.e., the average of the curve over each time interval will be equal to the corresponding input price. Partially overlapping products in any combination are handled without problems. Typical overlaps include month/quarters, quarter/years, a twelve month April-Mars period overlapping with several other products, etc. If there are complete overlaps, e.g. a year and all quarters of the same year, it may be mathematically impossible to fit all prices (unless they are perfectly consistent). These cases will be clearly identified by the algorithm (and the curve will by default be fitted to the prices with the finer time resolution). If the prices are tradable, this may represent an arbitrage opportunity.

Use the Information Contained in the Bid/Offer Spreads

If the input prices are available with a bid/offer spread, the curve may be fitted within the spread instead of to the exact mid prices. This provides more freedom for the algorithm, normally resulting in a smoother curve. This will also deal better with non-liquid prices having wide spreads. The algorithm will give products with wide spreads reduced effect on the curve compared to products with narrow spreads. If the price of a product can not be fitted within the spread, this will be identified by the algorithm and may indicate a trading opportunity. Matrics also allows the user to customize completely which products should be included in the curve fitting, either by specifying things like moving “first 3 months”, “next 2 quarters”, etc, or by specifying each individual product by simple tick-off.

Keep Track of Your Curves in Live Charts

Live charts of any forward curve are available simply by dropping the index on an open chart. The chart can display both the smooth curve and the input prices used to construct the curve. This can be used by traders for detecting trading opportunities from prices that are mispriced compared to the general slope of the curve.

Easily Configure Curves for Your Non-Standard Indices

The freight market contains a lot of non-liquid indices with limited or no available forward market rates. In the dry market, for example, most of the paper liquidity is concentrated in the average routes. Physical freight contracts (CoAs), on the other hand, should be priced with respect to their closest single routes. For organizations with physical exposure, it is thus essential to have consistent curves for all the single routes. These curves should incorporate historical relations between the single routes and the averages, their starting points should be consistent with the current spot prices, and they should fulfill the average relation implicit in the definition of the average route. All these issues are handled by Matrics. The non-liquid curves are defined as functions of the more liquid ones. Each curve can be defined in terms of any number of other curves, and the relations can be nested to any desired level. The coefficients in the relations can be estimated from historical spot price data.

Incorporate Seasonal Effects

Seasonal variation can easily be incorporated into the curves. Seasonal patterns can be estimated from historical spot data or entered by the user. The seasonality will not override any of the provided market prices, but will add additional structure to the end of the curve where the market prices have lower granularity.

Do You Have a Fundamental View That is Different from the Market?

An organization will often need different curve sets for different purposes. In Matrics, any number of curve sets can be defined at the same time. One can for example have a “real time” set using intra-day prices collected from brokers, an “reference” set using Imarex closing prices from yesterday, and a “fundamental” set using the results from a fundamental model reflecting the long-term price assumptions of the organization. Users can easily switch between the different curve sets using a simple drop-down menu and compare the effects on individual contract values or portfolio reports.

Example: PM4TC forward curve fitted within bid/offer and with estimated seasonal profile
Curve generator example 1
Example: P3A forward curve estimated from PM4TC
Curve generator example 2
Example: PM4TC curve fitted to all Imarex closing prices
Curve generator example 3
Example: PM4TC curve with non-liquid prices excluded
Curve generator example 4