A Model for Solar Renewable Energy Certificates:

Transcription

1 A Model for Solar Renewable Energy Certificates: Shining some light on price dynamics and optimal market design Michael Coulon (work at Princeton University with Javad Khazaei & Warren Powell) August 15th, 2013 Workshop on Electricity, Energy and Commodities Risk Management Field s Institute, Toronto, Canada M.Coulon@sussex.ac.uk University of Sussex Toronto, Aug 15th 2013 p.1/27

2 Carbon Market Outlook Outlook for EU market bleak right now... (Apr 2013 Economist article)!"#$%&'()%!"#$%&'()*#$+,$*#%,*-$.)*,/#01$2&*3,4$-&*5#+$6'(($*#7#*3#*&+#$*,)48$+"#$6,*(8$!"#$%&'($%&)*$+,#-.$'(/$"#01'$/20'0-1$!$ $ On the other hand, other regions are developing (eg, California, China). Toronto, Aug 15th 2013 p.2/27

3 Renewable Energy Certificates (RECs) In the US, about 30 states recently introduced a Renewable Portfolio Standard (RPS). About 10 have set up markets for tradeable certificates called SRECs (or more generally RECs) to achieve these RPS targets. (map taken from: US DoE-NREL report by Bird, Heeter, Kreycik, 2011) Toronto, Aug 15th 2013 p.3/27

4 Renewable Energy Certificates (RECs) While cap-and-trade markets have struggled in recently (low prices, political stalemates, etc.), a new environmental market is growing. How does it work? Toronto, Aug 15th 2013 p.4/27

5 Renewable Energy Certificates (RECs) While cap-and-trade markets have struggled in recently (low prices, political stalemates, etc.), a new environmental market is growing. How does it work? Government sets increasing requirements on % solar power in the generation mix each future year. (ie, set R (1),R (2),... for yrs 1, 2,..) Toronto, Aug 15th 2013 p.4/27

6 Renewable Energy Certificates (RECs) While cap-and-trade markets have struggled in recently (low prices, political stalemates, etc.), a new environmental market is growing. How does it work? Government sets increasing requirements on % solar power in the generation mix each future year. (ie, set R (1),R (2),... for yrs 1, 2,..) Solar generators are issued SRECs (solar renewable energy certificates) for each MWh of power generated and can sell these in the market. Toronto, Aug 15th 2013 p.4/27

7 Renewable Energy Certificates (RECs) While cap-and-trade markets have struggled in recently (low prices, political stalemates, etc.), a new environmental market is growing. How does it work? Government sets increasing requirements on % solar power in the generation mix each future year. (ie, set R (1),R (2),... for yrs 1, 2,..) Solar generators are issued SRECs (solar renewable energy certificates) for each MWh of power generated and can sell these in the market. All load serving entities (utilities) must submit sufficient SRECs each year to meet requirement, or else pay a penalty (say, π (1),π (2),...). Toronto, Aug 15th 2013 p.4/27

8 Renewable Energy Certificates (RECs) While cap-and-trade markets have struggled in recently (low prices, political stalemates, etc.), a new environmental market is growing. How does it work? Government sets increasing requirements on % solar power in the generation mix each future year. (ie, set R (1),R (2),... for yrs 1, 2,..) Solar generators are issued SRECs (solar renewable energy certificates) for each MWh of power generated and can sell these in the market. All load serving entities (utilities) must submit sufficient SRECs each year to meet requirement, or else pay a penalty (say, π (1),π (2),...). SRECs have a vintage year but can typically be banked for several future years. (currently 5 year life in NJ, so 4 banking chances). Toronto, Aug 15th 2013 p.4/27

9 Renewable Energy Certificates (RECs) While cap-and-trade markets have struggled in recently (low prices, political stalemates, etc.), a new environmental market is growing. How does it work? Government sets increasing requirements on % solar power in the generation mix each future year. (ie, set R (1),R (2),... for yrs 1, 2,..) Solar generators are issued SRECs (solar renewable energy certificates) for each MWh of power generated and can sell these in the market. All load serving entities (utilities) must submit sufficient SRECs each year to meet requirement, or else pay a penalty (say, π (1),π (2),...). SRECs have a vintage year but can typically be banked for several future years. (currently 5 year life in NJ, so 4 banking chances). A market-based alternative to direct subsidies for clean technologies! Toronto, Aug 15th 2013 p.4/27

10 Renewable Energy Certificates (RECs) While cap-and-trade markets have struggled in recently (low prices, political stalemates, etc.), a new environmental market is growing. How does it work? Government sets increasing requirements on % solar power in the generation mix each future year. (ie, set R (1),R (2),... for yrs 1, 2,..) Solar generators are issued SRECs (solar renewable energy certificates) for each MWh of power generated and can sell these in the market. All load serving entities (utilities) must submit sufficient SRECs each year to meet requirement, or else pay a penalty (say, π (1),π (2),...). SRECs have a vintage year but can typically be banked for several future years. (currently 5 year life in NJ, so 4 banking chances). A market-based alternative to direct subsidies for clean technologies! But... if prices are too volatile, it can be very risky for solar investors relying on revenues from selling SRECs, counteracting the goal of the market = Market design very important! Toronto, Aug 15th 2013 p.4/27

11 The New Jersey SREC market The New Jersey SREC market is the biggest in the US (among about 10 states; similar markets for green certificates also exist in Europe and Asia) Most ambitious target of over 4% solar energy by Highest recorded prices so far at about $700 per SREC. Rapid growth witnessed in solar installations in recent years. (plot below from NJ Clean Energy) Installed Capacity (MW dc) 1,200 1, NJ Solar Installed Capacity by Year Capacity Added Total Installed Capacity Toronto, Aug 15th 2013 p.5/27

12 The New Jersey SREC market The rules of the NJ market have been changed many times. Just a summary: Oldest Rules 2008 change 2012 change Energy True-up (no banking) (3-year life) (5-year life) Year Period R π R π R π mon 32, mon 65, mon 130, , mon 195, , mon 306, mon 442, , mon 596, , mon 772, ,707, mon 965, ,071, mon 115, ,360, mon 2,613, mon 2,829, Toronto, Aug 15th 2013 p.6/27

13 The New Jersey SREC market What about historical prices? Very high (near π) until very recently... SREC prices ($) EY 2007 EY 2008 EY 2009 EY 2010 EY 2011 EY 2012 EY 2013 SACP date Toronto, Aug 15th 2013 p.7/27

14 The New Jersey SREC market Historical (monthly) issuance data easily available online. Solar generation is growing fast (faster thanr), with clear seasonality... will the trend continue? annualized SREC issuance rate (1,000 MWh) EY 2007 EY 2008 EY 2009 EY 2010 EY 2011 EY 2012 EY 2013 Requirement date Toronto, Aug 15th 2013 p.8/27

15 Stochastic models for SREC prices How can we model an SREC price p y t (for vintage year y N)? Essentially no literature (useful reports, websites, but not price models!) Instead we draw on strong parallels with carbon emissions markets (with supply and demand reversed... here government fixes demand) Toronto, Aug 15th 2013 p.9/27

16 Stochastic models for SREC prices How can we model an SREC price p y t (for vintage year y N)? Essentially no literature (useful reports, websites, but not price models!) Instead we draw on strong parallels with carbon emissions markets (with supply and demand reversed... here government fixes demand) Consider a single-year case t [y 1, y] (no banking). Like carbon, SRECs are traded financial contracts, and thus martingales under Q At the compliance date, they should be worth either 0 or the penalty π y t Toronto, Aug 15th 2013 p.9/27

17 Stochastic models for SREC prices How can we model an SREC price p y t (for vintage year y N)? Essentially no literature (useful reports, websites, but not price models!) Instead we draw on strong parallels with carbon emissions markets (with supply and demand reversed... here government fixes demand) Consider a single-year case t [y 1, y] (no banking). Like carbon, SRECs are traded financial contracts, and thus martingales under Q At the compliance date, they should be worth either 0 or the penalty π y t Therefore, for t [y 1,y], p y t = e r(y t) π y te t [ 1 { y y 1 g udu<r y t } ], { y = e r(y t) πtp y g u du < R y t t t y 1 } g u du, where g t is the annualized solar generation rate (ie, SREC issuance rate). Toronto, Aug 15th 2013 p.9/27

18 Structural model for SREC prices Next step: Include k years of banking, such that a vintage year y SREC is valid for compliance at times t {y,y +1,...,y +k} Then the price today is a max over all future shortage probabilities: p y t = max v { t, t +1,...,y+k} e r(v t) πte v [ ] t 1{bv =0} where b t is the accumulated SREC supply (this year s plus banked): b t = ( max 0,b t 1 + ) t t 1 g udu Rt t t N, b t 1 + t t 1 g udu t / N. (Note that at t N,b t = 0 if the requirement is not met.) Toronto, Aug 15th 2013 p.10/27

19 Structural model for SREC prices Next step: Include k years of banking, such that a vintage year y SREC is valid for compliance at times t {y,y +1,...,y +k} Then the price today is a max over all future shortage probabilities: p y t = max v { t, t +1,...,y+k} e r(v t) πte v [ ] t 1{bv =0} where b t is the accumulated SREC supply (this year s plus banked): b t = ( max 0,b t 1 + ) t t 1 g udu Rt t t N, b t 1 + t t 1 g udu t / N. (Note that at t N,b t = 0 if the requirement is not met.) Final step: A stochastic model for solar generation rate g t? Toronto, Aug 15th 2013 p.10/27

20 NJ SREC issuance data Log plot of total monthly issuance shows some noise but also a clear trend (slope = 0.64) and seasonality: log e (g t ) original fitted log e (g^t) Year Like for electricity demand, perhaps modelg t with an OU process plus a trend and cosines? Anything missing? Toronto, Aug 15th 2013 p.11/27

21 Structural model for SREC prices Yes, feedback of SREC prices on generation growth is crucial! Toronto, Aug 15th 2013 p.12/27

22 Structural model for SREC prices Yes, feedback of SREC prices on generation growth is crucial! We first fit seasonality and Gaussian noise term ε t : g t = ĝ t (p)exp(a 1 sin(4πt)+a 2 cos(4πt)+a 3 sin(2πt)+a 4 cos(2πt)+ε t ), Toronto, Aug 15th 2013 p.12/27

23 Structural model for SREC prices Yes, feedback of SREC prices on generation growth is crucial! We first fit seasonality and Gaussian noise term ε t : g t = ĝ t (p)exp(a 1 sin(4πt)+a 2 cos(4πt)+a 3 sin(2πt)+a 4 cos(2πt)+ε t ), We then assume that the average annual generation rate ĝ t grows as: ln(ĝ t+ t ) ln(ĝ t ) t = a 5 +a 6 p t, for a 5 R,a 6 > 0, where a 6 captures sensitivity to prices (degree of feedback). Toronto, Aug 15th 2013 p.12/27

24 Structural model for SREC prices Yes, feedback of SREC prices on generation growth is crucial! We first fit seasonality and Gaussian noise term ε t : g t = ĝ t (p)exp(a 1 sin(4πt)+a 2 cos(4πt)+a 3 sin(2πt)+a 4 cos(2πt)+ε t ), We then assume that the average annual generation rate ĝ t grows as: ln(ĝ t+ t ) ln(ĝ t ) t = a 5 +a 6 p t, for a 5 R,a 6 > 0, where a 6 captures sensitivity to prices (degree of feedback). p t allows for dependence on historical average prices, not just today s: p y t = δp y t +(1 δ) p y t t and p y 0 = py 0 Toronto, Aug 15th 2013 p.12/27

25 Structural model for SREC prices Yes, feedback of SREC prices on generation growth is crucial! We first fit seasonality and Gaussian noise term ε t : g t = ĝ t (p)exp(a 1 sin(4πt)+a 2 cos(4πt)+a 3 sin(2πt)+a 4 cos(2πt)+ε t ), We then assume that the average annual generation rate ĝ t grows as: ln(ĝ t+ t ) ln(ĝ t ) t = a 5 +a 6 p t, for a 5 R,a 6 > 0, where a 6 captures sensitivity to prices (degree of feedback). p t allows for dependence on historical average prices, not just today s: p y t = δp y t +(1 δ) p y t t and p y 0 = py 0 This completes the model. We can now solve by dynamic programming. (Between years p y t = e r t E Q t [p y t+ t ], while jumps can occur at t N.) Toronto, Aug 15th 2013 p.12/27

26 Summary of the Algorithm Recall: Firstly the price today as a maximum over expected payoffs: p y t = max v { t, t +1,...,y+k} e r(v t) πte v [ ] t 1{bv =0}. Discretize and initialize p y T (b T,ĝ T ) = 1 {bt =0} at T = y +k. Then: Toronto, Aug 15th 2013 p.13/27

27 Summary of the Algorithm Recall: Firstly the price today as a maximum over expected payoffs: p y t = max v { t, t +1,...,y+k} e r(v t) πte v [ ] t 1{bv =0}. Discretize and initialize p y T (b T,ĝ T ) = 1 {bt =0} at T = y +k. Then: Fort / N, solve p y t = e r t E Q t [p y t+ t ], a fixed point problem with p y t = ĝ t+ t = b t+ t = RHS. ) Fort N, solve p y t = max (π t1 t {bt =0}, e r t E Q t [p y t+ t ] Toronto, Aug 15th 2013 p.13/27

28 Summary of the Algorithm Recall: Firstly the price today as a maximum over expected payoffs: p y t = max v { t, t +1,...,y+k} e r(v t) πte v [ ] t 1{bv =0}. Discretize and initialize p y T (b T,ĝ T ) = 1 {bt =0} at T = y +k. Then: Fort / N, solve p y t = e r t E Q t [p y t+ t ], a fixed point problem with p y t = ĝ t+ t = b t+ t = RHS. ) Fort N, solve p y t = max (π t1 t {bt =0}, e r t E Q t [p y t+ t ] Analogously for carbon (emissionse t, allowance price A t ), the FBSDE: de t = µ E (A t, )dt, E 0 = 0, da t = ra t dt+z t dw t A T = π1 {ET κ}, where the emissions drift µ E (A t, ) is decreasing ina t. Toronto, Aug 15th 2013 p.13/27

29 Results of structural model Solving algorithm produces a surface P t (b t,ĝ t ) for each time. For 2013 SRECs near the end of the first year: price x 10 6 accumulated supply of SRECs x 10 6 SREC issuance rate Toronto, Aug 15th 2013 p.14/27

30 Results of structural model Same price surface but six months later: price x 10 6 accumulated supply of SRECs x 10 6 SREC issuance rate Toronto, Aug 15th 2013 p.15/27

31 Results of structural model As with carbon, price surface diffuses from its digital option shape at each compliance date (but not exactly a digital payoff if banking provides value): T 4.5 T 4 T 3.5 T 3 T 0.5 T SREC price cumulative SREC generation (b ) t x 10 6 Toronto, Aug 15th 2013 p.16/27

32 Results of structural model Sensitivity to feedback parameter a 6 : price ($) a 6 =1x10 4 (T 2.5) a 6 =1x10 4 (T 0.5) a 6 =7x10 4 (T 2.5) a =7x10 4 (T 0.5) 6 a 6 =15x10 4 (T 2.5) a 6 =15x10 4 (T 0.5) T (all cases) total SREC supply, b t (MWh) x 10 5 Toronto, Aug 15th 2013 p.17/27

33 Comparison to history After fitting parameters, we compare historical market vs model prices: Overall price behaviour through history reasonably encouraging Also, provides some evidence about the level of feedback in the market SREC price Observed Market Prices Toronto, 2013 Aug 15th 2013 p.18/27 date

34 Comparison to history Price elasticity parameter set toa 6 = throughout, except: For 2013A line,a 6 = (low feedback) For 2013B line, a 6 = (high feedback) SREC price A 2013B Model Prices date Toronto, Aug 15th 2013 p.19/27

35 Policy Analysis SREC markets (just like cap-and-trade) are very sensitive to market design. For example, choosing an appropriate requirement growth schedule: Expected SREC price (vintage 2014) current exponential Month (from the start of EY2014) Toronto, Aug 15th 2013 p.20/27

36 Policy Analysis A larger number of banking years clearly produces greater price stability: Standard deviation of SREC price (vintage 2014) Month (from the start of EY2014) Toronto, Aug 15th 2013 p.21/27

37 Policy Analysis - Other Ideas? Inherent instability (in both REC and carbon markets) is due to the digital payoff functions... why not try something smoother? (eg, the blue line below) SACP SRECs submitted at the compliance date Toronto, Aug 15th 2013 p.22/27

38 Penalty Function: Step vs Slope A sloped penalty function implies: A non-trivial (model-dependent) banking decision each year A resulting threshold analogous to Am. options exercise boundary Simulated paths reveal greater stability: Step ( : 0) Sloped ( : ) Expected SREC price (vintage 2013) Expected SREC price (vintage 2013) th Percentile Mean 90thPercentile Month (from the start of EY2013) 50 10th Percentile Mean 90thPercentile Month (from the start of EY2013) Toronto, Aug 15th 2013 p.23/27

39 Penalty Function: Step vs Slope Long-term simulations of different vintages reveal that with a sloped (graduated) penalty policy: Lower volatility, more stable prices, fewer sudden price drops Much smaller price gaps between different vintage years Toronto, Aug 15th 2013 p.24/27

40 Penalty Function: Step vs Slope Long-term simulations of different vintages reveal that with a sloped (graduated) penalty policy: Lower volatility, more stable prices, fewer sudden price drops Much smaller price gaps between different vintage years SREC price (different vintage years) Month (from the start of EY2014) SREC price (different vintage years) Month (from the start of EY2014) Simulations above use the same set of random numbers but for the step case ( = 0) on the left and slope case ( = 500 GWh) on the right. Toronto, Aug 15th 2013 p.24/27

41 Penalty Function: Step vs Slope Mean of simulations reveals similar patterns (again = 0 on left, = 500 GWh on right) Expected SREC price (different vintage years) Month (from the start of EY2014) Expected SREC price (different vintage years) Month (from the start of EY2014) Note: Why do the annual drops in mean price not clash with no arbitrage? Expectation is taken over all paths, including those for which banking is not optimal (ie, SRECs should all be used up for compliance) Hence no price drops in practice as that vintage would disappear. Toronto, Aug 15th 2013 p.25/27

42 Penalty Function: Step vs Slope Mean of simulations reveals similar patterns (again = 0 on left, = 500 GWh on right) Expected SREC price (different vintage years) Month (from the start of EY2014) Expected SREC price (different vintage years) Month (from the start of EY2014) Note: Why do the annual drops in mean price not clash with no arbitrage? Expectation is taken over all paths, including those for which banking is not optimal (ie, SRECs should all be used up for compliance) Hence no price drops in practice as that vintage would disappear. Toronto, Aug 15th 2013 p.25/27

43 Other Policy Options While useful for smoothing dynamics, changing the penalty alone does not address long-term supply and demand imbalances which have often trigger new legislation. Any other way? Toronto, Aug 15th 2013 p.26/27

44 Other Policy Options While useful for smoothing dynamics, changing the penalty alone does not address long-term supply and demand imbalances which have often trigger new legislation. Any other way? A dynamically adaptive requirement level each year. For example, set R y = R y +λ ( b y 1 ǫ R y 1), λ (0,1). Toronto, Aug 15th 2013 p.26/27

45 Other Policy Options While useful for smoothing dynamics, changing the penalty alone does not address long-term supply and demand imbalances which have often trigger new legislation. Any other way? A dynamically adaptive requirement level each year. For example, set R y = R y +λ ( b y 1 ǫ R y 1), λ (0,1). Policy could work in conjunction with a function π(r) for adaptive penalties which gradually reduce as long-term solar targets approach. Toronto, Aug 15th 2013 p.26/27

46 Other Policy Options While useful for smoothing dynamics, changing the penalty alone does not address long-term supply and demand imbalances which have often trigger new legislation. Any other way? A dynamically adaptive requirement level each year. For example, set R y = R y +λ ( b y 1 ǫ R y 1), λ (0,1). Policy could work in conjunction with a function π(r) for adaptive penalties which gradually reduce as long-term solar targets approach. Unrealistically complicated? Currently in Massachusetts, they use: Total Compliance Obligation 2013 = Total Compliance Obligation [Total SRECs Generated (projected) SRECs Generated (actual) 2011] x Banked Volume Auction Volume ACP Volume 2011 Toronto, Aug 15th 2013 p.26/27

47 Other Policy Options While useful for smoothing dynamics, changing the penalty alone does not address long-term supply and demand imbalances which have often trigger new legislation. Any other way? A dynamically adaptive requirement level each year. For example, set R y = R y +λ ( b y 1 ǫ R y 1), λ (0,1). Policy could work in conjunction with a function π(r) for adaptive penalties which gradually reduce as long-term solar targets approach. Unrealistically complicated? Currently in Massachusetts, they use: Total Compliance Obligation 2013 = Total Compliance Obligation [Total SRECs Generated (projected) SRECs Generated (actual) 2011] x Banked Volume Auction Volume ACP Volume 2011 Finally, in addition to this formula for R, Mass implements a $300 fixed-price auction each year, as a form of price floor mechanism. Toronto, Aug 15th 2013 p.26/27

48 Market Design Ideas Stabilizing prices (to encourage more investment) without defeating the point of the market is really striking a balance between price and quantity targets. In summary, what design tools can regulators consider? Toronto, Aug 15th 2013 p.27/27

49 Market Design Ideas Stabilizing prices (to encourage more investment) without defeating the point of the market is really striking a balance between price and quantity targets. In summary, what design tools can regulators consider? Continue to stretch the banking life of SRECs Toronto, Aug 15th 2013 p.27/27

50 Market Design Ideas Stabilizing prices (to encourage more investment) without defeating the point of the market is really striking a balance between price and quantity targets. In summary, what design tools can regulators consider? Continue to stretch the banking life of SRECs Change the digital payoff in the implementation of the penalty to something smoother? (slope instead of step) Toronto, Aug 15th 2013 p.27/27

51 Market Design Ideas Stabilizing prices (to encourage more investment) without defeating the point of the market is really striking a balance between price and quantity targets. In summary, what design tools can regulators consider? Continue to stretch the banking life of SRECs Change the digital payoff in the implementation of the penalty to something smoother? (slope instead of step) Allow next year s requirement to adapt / respond to this year s surplus / shortage? (tried by Massachusetts already) Toronto, Aug 15th 2013 p.27/27

52 Market Design Ideas Stabilizing prices (to encourage more investment) without defeating the point of the market is really striking a balance between price and quantity targets. In summary, what design tools can regulators consider? Continue to stretch the banking life of SRECs Change the digital payoff in the implementation of the penalty to something smoother? (slope instead of step) Allow next year s requirement to adapt / respond to this year s surplus / shortage? (tried by Massachusetts already) Allow next year s penalty to adapt / respond to this year s prices? (tried by Pennsylvania already) Toronto, Aug 15th 2013 p.27/27

53 Market Design Ideas Stabilizing prices (to encourage more investment) without defeating the point of the market is really striking a balance between price and quantity targets. In summary, what design tools can regulators consider? Continue to stretch the banking life of SRECs Change the digital payoff in the implementation of the penalty to something smoother? (slope instead of step) Allow next year s requirement to adapt / respond to this year s surplus / shortage? (tried by Massachusetts already) Allow next year s penalty to adapt / respond to this year s prices? (tried by Pennsylvania already) Establish an organization to periodically reassess requirement? (like central banks for money supply!) Toronto, Aug 15th 2013 p.27/27

54 Market Design Ideas Stabilizing prices (to encourage more investment) without defeating the point of the market is really striking a balance between price and quantity targets. In summary, what design tools can regulators consider? Continue to stretch the banking life of SRECs Change the digital payoff in the implementation of the penalty to something smoother? (slope instead of step) Allow next year s requirement to adapt / respond to this year s surplus / shortage? (tried by Massachusetts already) Allow next year s penalty to adapt / respond to this year s prices? (tried by Pennsylvania already) Establish an organization to periodically reassess requirement? (like central banks for money supply!) Some promising ideas, but details are tricky and more work on understanding and modeling the resulting price dynamics is crucial! Toronto, Aug 15th 2013 p.27/27