Use an Arbitrage-Free Forward Curve Before PCA Hedging
Summary
The document addresses how overlapping delivery periods can affect principal component analysis of gas forward curves. A monthly contract may also be included inside a quarterly or calendar contract, so treating all quoted contracts as independent curve points can introduce correlations that reflect contract construction rather than distinct market movements.
The proposed method first builds an arbitrage-free curve at the finest desired delivery granularity. It uses more liquid contracts as inputs and derives prices for omitted periods from broader contracts; repeating this across dates produces a consistent monthly history for PCA. After identifying the curve's principal movements, the researcher finds a feasible combination of tradable products to hedge the target exposure. The example explains why a hedge containing both a single month and a quarter may represent exposure to another month implied by the curve structure. The recommendation is conceptual and offers no empirical comparison or detailed optimization procedure; its value depends on liquidity choices and reliable pricing relationships.
Key ideas
- Overlapping delivery contracts can make raw forward-curve PCA reflect structural price relationships.
- Construct an arbitrage-free curve at the finest delivery granularity needed for the analysis.
- Use liquid quoted contracts to infer prices for less liquid or omitted delivery periods.
- Run PCA on the consistently constructed curve history, then map its movements to tradable hedge instruments.
- The method depends on contract liquidity and the quality of the inferred prices.
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Full text
# Principal Components Analysis on overlapping contracts # Principal Components Analysis on overlapping contracts I am conducting several PCAs on the gas forward curves (months, quarters, seasons, calendars) for hedging purposes which give me some rather reasonable and stable results. However, these contracts overlap with each other, for example: in December the front month contract is a part of both the front quarter contract and front calendar contract. I have often come across analysis conducted on yield curves where contracts overlap as well and nobody mentions it.We are questioning ourselves about the cleanliness of that procedure and these overlaps. My opinion is that that feature only add more correlation into prices which is not undesired. Any idea/suggestion ? Thanks a lot ! I am conducting several PCAs on the gas forward curves (months, quarters, seasons, calendars) for hedging purposes which give me some rather reasonable and stable results. However, these contracts overlap with each other, for example: in December the front month contract is a part of both the front quarter contract and front calendar contract. I have often come across analysis conducted on yield curves where contracts overlap as well and nobody mentions it. ## Answer by ZRH (score 6, accepted) https://quant.stackexchange.com/a/43965 I would do as follows: A) First do PCA on an arbitrage-free monthly curve (assuming the most granular contract you will use is individual months). To ensure no arbitrages, you will need to drop out certain contracts, I would drop the most illiquid ones. To give you an example, if you are in Dec, you might see Jan, Feb and Mar quoted, but also Q1. In this case, I would use Jan and Feb, and determine the arbitrage-free Mar price by using Q1. In the same spirit, you would then use Q1, Q2 and Q3, and determine Q4 via using the calendar year contract. Doing that for multiple days allows you to do PCA to determine curve dynamics down to the granularity which you have in the market. B) Once you have determined the principal components of the curve movement, you take the product that you want to hedge and look at the optimal combination of products that you can actually trade in order to work out your hedge. I think that this way of doing it should avoid spurious results, since the curve that you put into the PCA has been cleanly constructed. To come back to your example, if you are in Dec, and your optimization suggests a hedge which is in part Jan and in part Q1, then it should be because the PCA suggests that you also need to have some Mar contract in the hedge.
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