Streetwise Professor

June 3, 2019

Renewables VPPAs: An Interesting Pricing Problem For Aspiring Scholars

Filed under: Climate Change,Commodities,Derivatives,Economics,Energy — cpirrong @ 7:13 pm

Virtual Power Purchasing Agreements (VPPAs) have been around for a while, and play a particularly important role in securing financing for renewable energy projects, as this article from Reuters regarding VPPAs in Europe indicates. They are essentially long term swaps whereby one party (e.g., a wind or solar operation) receives a fixed price for power, and pays a floating price, usually based (in the US) on the spot price in an RTO/ISO market (e.g., PJM, or MISO).

These contracts present interesting pricing issues because of the unique nature of electricity as a commodity, and the unique nature of renewable generation in particular. Electricity is not an asset per se, and electricity price risk is not hedgeable, even theoretically, through a dynamic trading strategy in the way that the price risk in a stock option is. This means that electricity markets are “incomplete,” and that Black-Scholes-Merton-like formulas that derive prices that do not depend on risk premia do not exist for power derivatives.

The risk premia embedded in power prices can be large, though they have been falling over the years. I wrote extensively about this subject for about 10 years (late-90s to late-00s), including this article. That paper provides a way of extracting risk premia from the prices of traded claims (e.g., monthly power forward contracts). One virtue of that approach is that the primary state variable in the model is not price, but load (which is translated into price via the supply curve). Thus, the relevant price of risk is the price of load risk, which can be used in the valuation of load-dependent claims. Such claims could be full requirements deals, for example.

One challenge to the approach is that the realistic horizon of the market price of risk function estimate is that of the visible forward curve, which is typically far less than the maturity of long term electricity deals. The prices in such contracts effectively reflect a market price of risk negotiated between the two parties, in the absence of corresponding forward curve data.

Renewables VPPAs face an even bigger challenge: the variability of the output of a renewables asset. There is not only price risk (or market load risk) associated with a given region: there is the output risk of the facility, which may be material given the vicissitudes of wind and sun. Thus, the dimensionality of the pricing problem is higher, which is a problem given that the methods I employed in my 2008 paper (co-authored by Martin Jermakyan) are subject to “the curse of dimensionality.”

Furthermore, given the joint dependency on market price (or load) and project output, these are correlation-dependent claims. That is, what is the dependence between market price and wind output? This could be a particularly big issue given that high wind output is often associated with negative prices. Guaranteeing a fixed price therefore involves something of a wrong way risk.

The long tenor of VPPAs makes these issues even more devilish, given that pricing involves forecasting the relevant dynamics and parameters (including those associated with dependence among the state variables) over long horizons–horizons over which entry can occur and technology can change, making historical data of little relevance in estimation. Indeed, there is an element of endogeneity: the prices in VPPAs can affect the economics of entry, which can affect future price behavior, which is (theoretically, anyways) an input into the “right” VPPA fixed price.

All in all, a very interesting and challenging pricing problem, that like the simpler problems Martin and I tackled some years ago, require the use of advanced pricing techniques, numerical methods, and econometrics even to conceptualize, let alone solve. Sounds like an interesting problem–or problems–for aspiring scholars in energy pricing.

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  1. Problems whose solution defy the likes of the SWP go on my bucket list, or the revese bucket list. The f****et list.

    Comment by The Pilot — June 3, 2019 @ 9:19 pm

  2. @Pilot–LOL. And thanks šŸ˜‰

    Comment by cpirrong — June 3, 2019 @ 9:53 pm

  3. SWP:

    Vlad foresees no Hunt Bros to corner the VPPA market. In anonymity, they will be monikered as the Khunt Bros.

    Be well.

    VP VVP

    Comment by Vlad — June 4, 2019 @ 8:57 am

  4. I love economics, understand the concepts here, but once the deep math and econometrics start, Iā€™m outta here. Thanks for the thought experiment.

    Comment by The Pilot — June 4, 2019 @ 2:17 pm

  5. Long term evaluation of VPPAs is simpler than the short term. The fewer the liquid underliers, the simpler the analysis. in other words, there’s no need to forecast the underlying dynamic factors over the long term at all.

    Comment by Krzys — June 5, 2019 @ 12:15 pm

  6. I can’t download the paper to look at your math, but perhaps a good place to start is a change-of-variables substituting (load variability – supply variability) for the load variability and using “base” supply where supply was. I would guess that the statistics of supply variability are very different from load variability, so even if the PDE has a similar form, the actual price behavior could be very different.

    Comment by M. Rad. — June 12, 2019 @ 2:24 pm

  7. @M. Rad–Here’s a link to an earlier working paper version of the paper. The final version is pretty similar. I’d be interested in your comments. And yes, I’d considered looking at load net of renewables generation as the state variable.

    Comment by cpirrong — June 14, 2019 @ 9:16 am

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