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Forward Curves Modelling

Forward Curve Building & Fitting, Medium to Long Term Data & Curve Forecasting

Comprehensive forward curve fitting and data forecasting solutions

QR Forward Curve building module provides a unified and very powerful environment to model and forecast data as daily or monthly forward curves. Some examples are:

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    Daily spot, monthly forward and implied volatility curves for pricing points of any traded instrument with futures/forward market: energy, commodity, equity, FX, interest rate, indices, etc.
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    Forecast daily spot curves for prices on one hand, and volumes, meters and load on the other hand. The latter can be at the transactional or meter/hub level, or aggregated per any desired rules, e.g., market, region, business types such as supply or demand, etc.
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    Daily and monthly forecast of any data type, e.g., economic, operational, financial, trading, indices/indicators, AP, AR, billing data, etc.
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    Forward curve building outputs are displayed in a data panel in a web browser, in table formats and graphical plots, and can be exported in CSV format.
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    Automatic extrapolation allows to build curves years out, far beyond the initial data provided.
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    When there isn’t sufficient underlying data, we can define an index via mathematics formulas involving other base curves for which there are partial data quotes. Then point the spot, forward or load curve to the index.
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    The models we use are multi-frequency Fourier series. They capture multiple seasonal shapes, cycles, and trends. Automatic interpolation smoothly fills in missing quotes or gaps in the data alleviating illiquidity. In addition, users can further refine the forward curve forecast by inducing additional factors as mathematical formulae using other curves. These can be weather, economic factors, growth, CPI, etc.

Curve Fitting Job Automation

After validating and fine tuning a given forward curve model you can save it as an analytics job for re-use. Analytics jobs are each sandboxed and their parameters, inputs, and outputs saved. The parallel processor analytics engine can simultaneously execute multiple instances of such jobs. These can further be scheduled to launch automatically, providing automation of forward curve building or forecasting for trading support, risk management or asset optimization.

Advanced Curve Models

You can create and customize multiple forward curve models. The models are Fourier polynomials with multiple frequencies to capture multiple seasonal shapes and exponential or linear trend. For example, in energy and commodity markets, use a 6 month cycle to model summer/winter blocks, and a 12 month cycle for the shape to reproduce itself yearly. In FX and interest rate markets use a 2 to 4 year cycle, etc.

Forward Curve via Proxy Curves

Commodity and energy pricing points can have at most one liquid forward curve quoted in a future exchange. They lack forward market quotes at specific financial or physical locations or hubs. A friendly interface allows users to type in formulas (e.g., some weighted averages) involving other curves for which forward curve data is available, and point the forward curve of that pricing point to the formula. For example, the formula can involve some locational or broker curves as it's the case in many fuel, natural gas and food commodity markets. Consider this example in natural gas markets in North America. The forward curve of a local physical or financial gas hub can point to a weighted average: 35% on the very liquid futures contract HH, 45% on a much less liquid City Gate hub, and 20% on sparsely published Daily Rate, with the first two hubs having some base points attached to them: Average (0.35 * (HH + 0.25), 0.45*(City Gate + 0.15) + 0.20* Day Rate). The averaging function is sophisticated enough to handle the case of missing data points in some curves.

Inter/extra-polation Of Missing Quotes

Building forward/forecast curves using interpolation. In illiquid markets some forwards curves can have missing quotes or gaps, or quotes amalgamating several months. The system has advanced mathematical routines to interpolate for missing data while respecting all provided quotes. For example, you may have a combined Jan-Feb quote, followed by one spring Mar-Jun quote, and then nothing. Yet you need monthly forward curves to mark your portfolio to market. The System will interpolate accurately through all these missing points. Building forward/forecast curves using extrapolation. Once the model is calibrated as above, it can be projected forward well beyond the range of the initial data provided by the user for calibration, yet respecting the projected trend and cyclical shape. For example, you can provide only a 12 months forward curve for fitting or calibration, and build one for 15 years.

Model Calibration

Calibrate the Model. Once the model (Fourier series) is created, the system estimates its parameters by fitting through the data curve provided/entered by the user. The system offers great flexibility to make use of the best available data for calibration. The model can be made completely forward looking as in forward curve building for a pricing point. In this case the user can provide as calibration input data, today’s market curve from a data provided, albeit with gaps and limitations. When forward data is not readily available the model can be made backward looking. E.g., to forecast volume or load, you can point to historic load data as calibration input. Then curve fitting extracts its seasonal shape and trend to project it forward.