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 with Javad Khazaei & Warren Powell) January 15th, 2014 Essen, Germany University of Sussex Essen, Jan 15th 2014 p.1/38

2 Carbon Market Outlook Outlook for EU market bleak recently... (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). Essen, Jan 15th 2014 p.2/38

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) Essen, Jan 15th 2014 p.3/38

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? Essen, Jan 15th 2014 p.4/38

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,..) Essen, Jan 15th 2014 p.4/38

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. Essen, Jan 15th 2014 p.4/38

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),...). Essen, Jan 15th 2014 p.4/38

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). Essen, Jan 15th 2014 p.4/38

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! Essen, Jan 15th 2014 p.4/38

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! Essen, Jan 15th 2014 p.4/38

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 $700 per SREC. Rapid growth witnessed in solar installations in recent years. '$!!"!"#$%&'(&)*+,-&.--/01&203&40$3&56777-&89:;& '#!!" '!!!" &!!" %!!" $!!" #!!"!" #!!%" #!!(" #!!&" #!!)" #!'!" #!''" #!'#" #!'*" +,-./" Essen, Jan 15th 2014 p.5/38

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 1,150, ,360, mon 2,613, mon 2,829, Essen, Jan 15th 2014 p.6/38

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 Essen, Jan 15th 2014 p.7/38

14 The New Jersey SREC market Historical (monthly) issuance data easily available online. Solar generation has grown fast (faster thanr), with clear seasonality... will this continue? annualized SREC issuance rate (1,000 MWh) EY 2007 EY 2008 EY 2009 EY 2010 EY 2011 EY 2012 EY 2013 Requirement date Essen, Jan 15th 2014 p.8/38

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) Essen, Jan 15th 2014 p.9/38

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 Essen, Jan 15th 2014 p.9/38

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). Essen, Jan 15th 2014 p.9/38

18 Structural model for SREC prices Next step: Include τ years of banking, such that a vintage year y SREC is valid for compliance at times t {y,y +1,...,y +τ} Then the price today is a max over all future shortage probabilities: p y t = max v { t, t +1,...,y+τ} 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 (and only if) the requirement is not met.) Essen, Jan 15th 2014 p.10/38

19 Structural model for SREC prices Next step: Include τ years of banking, such that a vintage year y SREC is valid for compliance at times t {y,y +1,...,y +τ} Then the price today is a max over all future shortage probabilities: p y t = max v { t, t +1,...,y+τ} 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 (and only if) the requirement is not met.) Final step: A stochastic model for solar generation rate g t? Essen, Jan 15th 2014 p.10/38

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? Essen, Jan 15th 2014 p.11/38

21 NJ SREC issuance data Looking more closely at SREC generation growth (and in recent data): #!!*",!*" +!*" )!*" (!*" '!*" &!*" %!*" $!*" #!*"!*" 1#2)3."4567'8#-9##"':1!;'7$6<#')"='4.2)$'%$.9-5' -./"0123"45678"9#:5";-/<" $!!+" $!!," $!#!" $!##" $!#$" $!#%" $!#&"!"#$%&'(#)$'*+,"#'-.'/)&0' )!!" (!!" '!!" &!!" %!!" $!!" #!!"!" Clear relationship between growth rate and (1yr lagged) price! Essen, Jan 15th 2014 p.12/38

22 Structural model for SREC prices Indeed, feedback of SREC prices on generation growth is crucial! Essen, Jan 15th 2014 p.13/38

23 Structural model for SREC prices Indeed, 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 ), Essen, Jan 15th 2014 p.13/38

24 Structural model for SREC prices Indeed, 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). Essen, Jan 15th 2014 p.13/38

25 Structural model for SREC prices Indeed, 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 Essen, Jan 15th 2014 p.13/38

26 Structural model for SREC prices Indeed, 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.) Essen, Jan 15th 2014 p.13/38

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+τ} 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 +τ. Then: Essen, Jan 15th 2014 p.14/38

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+τ} 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 +τ. 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 ] Essen, Jan 15th 2014 p.14/38

29 Summary of the Algorithm Recall: Firstly the price today as a maximum over expected payoffs: p y t = max v { t, t +1,...,y+τ} 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 +τ. 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. Essen, Jan 15th 2014 p.14/38

30 Summary Comparison with Carbon Clearly many similarities with cap-and-trade, but also key differences: Feature Cap-and-trade SREC market Banking (typically) unrestricted finite number of times (e.g. 4) Borrowing within trading periods none Withdrawal Pay penalty plus Penalty (SACP) only one allowance debt Periodicities none solar generation seasonal Feedback power sector new construction fuel switching of solar generation Available data? challenging at EU level easy (at monthly freq) Correlated with? power, gas, coal, etc relatively separate for now! Essen, Jan 15th 2014 p.15/38

31 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 Essen, Jan 15th 2014 p.16/38

32 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 Essen, Jan 15th 2014 p.17/38

33 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 Essen, Jan 15th 2014 p.18/38

34 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 Essen, Jan 15th 2014 p.19/38

35 Results of structural model Sensitivity to feedback lag parameter δ: price ($) δ=0.01 (T 2.5) δ=0.01 (T 0.5) δ=0.1 (T 2.5) δ=0.1 (T 0.5) δ=1.0 (T 2.5) δ=1.0 (T 0.5) T (all cases) total SREC supply, b (MWh) t x 10 5 Essen, Jan 15th 2014 p.20/38

36 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 date Essen, Jan 15th 2014 p.21/38

37 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 Essen, Jan 15th 2014 p.22/38

38 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) Essen, Jan 15th 2014 p.23/38

39 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) Essen, Jan 15th 2014 p.24/38

40 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, sloped line below) SACP p 1 Cliff policy Sloped policy p 1 p 2 p 2 x SRECs Submitted 1 x 2 Example prices shown for submitted SRECsx 1 and x 2. Shaded rectangles = penalty paid. Essen, Jan 15th 2014 p.25/38

41 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 Price of SRECs of vintage y at timetnow calculated via p t,y = max ( f t (x t ),e r t E t [p y t+ t ]), for t y +τ (i.e. before expiry) where for t N, π t, x t < (1 λ)r t, f t (x t ) = π t π t 2λR t (x t (1 λ)r t ), (1 λ)r t x t < (1+λ)R t, 0 (1+λ)R t x t. Here x t is the optimal number of SRECs submitted at t. But optimal how? Essen, Jan 15th 2014 p.26/38

42 Social Welfare Problem Formally, we should expand our state variable S t to track the banked supply of each SREC vintage y, via vector (b t,y ) y. ThenS t = ((b t,y ) y,ĝ t, p t ), and decision variable (x t,y ) y. Let b t = t y=max{1, t τ} b t,y and x t = t y=max{1, t τ} x t,y. Optimal submission decisions x t maximize social welfare by solving: V t (S t ) = max x t xt E t e r(u t) f t (u)du, Maximizing the expected area under the inverse demand curve is equivalent to the minimizing the total expected penalty payments. Can show that u x t = max ( b t,t τ,min ( b t,f 1 (e r E t [f t+1 (x t+1 ) x t ]) )). 0 Essen, Jan 15th 2014 p.27/38

43 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 (often zero!) between different vintages Essen, Jan 15th 2014 p.28/38

44 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 (often zero!) between different vintages 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 (λ = 0) on the left and slope case (λ = 0.3) on the right. Essen, Jan 15th 2014 p.28/38

45 Penalty Function: Varying Slopes 20 simulations of 8yrs, with increasing values of λ (flattening slope): SREC price (different vintage years) SREC price (different vintage years) Month (from the start of EY2014) Month (from the start of EY2014) SREC price (different vintage years) SREC price (different vintage years) Month (from the start of EY2014) Month (from the start of EY2014) Essen, Jan 15th 2014 p.29/38

46 Penalty Function: Step vs Slope Mean of simulations reveals similar patterns (λ = 0 on left, λ = 0.3 on right) Expected SREC price (different vintage years) Expected SREC price (different vintage years) Month (from the start of EY2014) Month (from the start of EY2014) Note: Why do the annual drops in mean price not clash with no arbitrage? Essen, Jan 15th 2014 p.30/38

47 Penalty Function: Step vs Slope Mean of simulations reveals similar patterns (λ = 0 on left, λ = 0.3 on right) Expected SREC price (different vintage years) Expected SREC price (different vintage years) Month (from the start of EY2014) 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. Essen, Jan 15th 2014 p.30/38

48 Penalty Function: Step vs Slope Mean of simulations reveals similar patterns (λ = 0 on left, λ = 0.3 on right) Expected SREC price (different vintage years) Expected SREC price (different vintage years) Month (from the start of EY2014) 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. Note: Why do all vintages seem to have identical prices throughout? Essen, Jan 15th 2014 p.30/38

49 Penalty Function: Step vs Slope At first this seems counter-intuitive, since newer SRECs clearly have more exercise opportunities left than older vintages. However, Essen, Jan 15th 2014 p.31/38

50 Penalty Function: Step vs Slope At first this seems counter-intuitive, since newer SRECs clearly have more exercise opportunities left than older vintages. However, Proposition: If λ > 0 and x t = X t (S t ) is an optimal policy at timet N, and x t > b t,t τ for all t N, all SREC vintages have the same price. Essen, Jan 15th 2014 p.31/38

51 Penalty Function: Step vs Slope At first this seems counter-intuitive, since newer SRECs clearly have more exercise opportunities left than older vintages. However, Proposition: If λ > 0 and x t = X t (S t ) is an optimal policy at timet N, and x t > b t,t τ for all t N, all SREC vintages have the same price. Proof: Rather lengthy, requires several other results first. Essen, Jan 15th 2014 p.31/38

52 Penalty Function: Step vs Slope At first this seems counter-intuitive, since newer SRECs clearly have more exercise opportunities left than older vintages. However, Proposition: If λ > 0 and x t = X t (S t ) is an optimal policy at timet N, and x t > b t,t τ for all t N, all SREC vintages have the same price. Proof: Rather lengthy, requires several other results first. Intuition: As soon as there is some slope (λ = 0), market participants essentially get to choose any price in[0,π t ] at t N by choosing x t Essen, Jan 15th 2014 p.31/38

53 Penalty Function: Step vs Slope At first this seems counter-intuitive, since newer SRECs clearly have more exercise opportunities left than older vintages. However, Proposition: If λ > 0 and x t = X t (S t ) is an optimal policy at timet N, and x t > b t,t τ for all t N, all SREC vintages have the same price. Proof: Rather lengthy, requires several other results first. Intuition: As soon as there is some slope (λ = 0), market participants essentially get to choose any price in[0,π t ] at t N by choosing x t Ifp t is too high or low relative to expected prices just after compliance, x t adjusts to bring these into balance. Essen, Jan 15th 2014 p.31/38

54 Penalty Function: Step vs Slope At first this seems counter-intuitive, since newer SRECs clearly have more exercise opportunities left than older vintages. However, Proposition: If λ > 0 and x t = X t (S t ) is an optimal policy at timet N, and x t > b t,t τ for all t N, all SREC vintages have the same price. Proof: Rather lengthy, requires several other results first. Intuition: As soon as there is some slope (λ = 0), market participants essentially get to choose any price in[0,π t ] at t N by choosing x t Ifp t is too high or low relative to expected prices just after compliance, x t adjusts to bring these into balance. Hence utilities choose to pay a penalty even when there is a surplus! (pay a small penalty and bank more, to reduce future penalties) Essen, Jan 15th 2014 p.31/38

55 Penalty Function: Step vs Slope At first this seems counter-intuitive, since newer SRECs clearly have more exercise opportunities left than older vintages. However, Proposition: If λ > 0 and x t = X t (S t ) is an optimal policy at timet N, and x t > b t,t τ for all t N, all SREC vintages have the same price. Proof: Rather lengthy, requires several other results first. Intuition: As soon as there is some slope (λ = 0), market participants essentially get to choose any price in[0,π t ] at t N by choosing x t Ifp t is too high or low relative to expected prices just after compliance, x t adjusts to bring these into balance. Hence utilities choose to pay a penalty even when there is a surplus! (pay a small penalty and bank more, to reduce future penalties) Only if the optimal decision x t falls belowb t,t τ (an unrealistically high surplus), can a price difference between vintages occur, as it s better to submit b t,t τ than let SRECs expire! Essen, Jan 15th 2014 p.31/38

56 Other Policy Options While useful for smoothing dynamics, a sloped penalty may not address long-term imbalances which often trigger new legislation. Any other ideas? Essen, Jan 15th 2014 p.32/38

57 Other Policy Options While useful for smoothing dynamics, a sloped penalty may not address long-term imbalances which often trigger new legislation. Any other ideas? A dynamically adaptive requirement level each year. For example, set R y = R y +α(b y 1 R y 1 ), 0 α 1,y N. Essen, Jan 15th 2014 p.32/38

58 Other Policy Options While useful for smoothing dynamics, a sloped penalty may not address long-term imbalances which often trigger new legislation. Any other ideas? A dynamically adaptive requirement level each year. For example, set R y = R y +α(b y 1 R y 1 ), 0 α 1,y N. Similar to dynamic allocation of allowances in Carmona et al (2010) Policy could work in conjunction with a function π(r) for adaptive penalties which gradually reduce as long-term solar targets approach. Essen, Jan 15th 2014 p.32/38

59 Other Policy Options While useful for smoothing dynamics, a sloped penalty may not address long-term imbalances which often trigger new legislation. Any other ideas? A dynamically adaptive requirement level each year. For example, set R y = R y +α(b y 1 R y 1 ), 0 α 1,y N. Similar to dynamic allocation of allowances in Carmona et al (2010) 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 Essen, Jan 15th 2014 p.32/38

60 Other Policy Options While useful for smoothing dynamics, a sloped penalty may not address long-term imbalances which often trigger new legislation. Any other ideas? A dynamically adaptive requirement level each year. For example, set R y = R y +α(b y 1 R y 1 ), 0 α 1,y N. Similar to dynamic allocation of allowances in Carmona et al (2010) 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. Essen, Jan 15th 2014 p.32/38

61 ADAPT policy proposal We hence suggest an approach called ADAPT (Adjustable Dynamic Assignment of Penalties and Targets) which provides regulators with two parameters (λ,α) as tools to control the levels of price volatility in the market. λ controlling the slope of the penalty function. α for controlling the responsiveness of the requirement. Ultimately different hybrid schemes between fixed price and fixed quantity! SACP SACP P t f t (x t ) λr t λr t P t αs t x t R t Submitted R t R t Submitted Essen, Jan 15th 2014 p.33/38

62 ADAPT policy: Varyingλand α 20 simulations, with(λ, α) given by (0, 0),(0.3, 0),(0, 0.5), and (0.3, 0.5): SREC price (different vintage years) SREC price (different vintage years) Month (from the start of EY2014) Month (from the start of EY2014) SREC price (different vintage years) Month (from the start of EY2014) SREC price (different vintage years) Month (from the start of EY2014) Essen, Jan 15th 2014 p.34/38

63 ADAPT policy: Varyingλand α The effect of also varyingαis less straightforward than that of λ: Taken by itself, increasing α can also help dampen price volatility. Essen, Jan 15th 2014 p.35/38

64 ADAPT policy: Varyingλand α The effect of also varyingαis less straightforward than that of λ: Taken by itself, increasing α can also help dampen price volatility. However, it can also counteract the effect of λ (since it means that banking more today ends up increasing future requirements!). Essen, Jan 15th 2014 p.35/38

65 ADAPT policy: Varyingλand α The effect of also varyingαis less straightforward than that of λ: Taken by itself, increasing α can also help dampen price volatility. However, it can also counteract the effect of λ (since it means that banking more today ends up increasing future requirements!). e.g. ifα = 1, the incentive to bank is completely cancelled out. Essen, Jan 15th 2014 p.35/38

66 ADAPT policy: Varyingλand α The effect of also varyingαis less straightforward than that of λ: Taken by itself, increasing α can also help dampen price volatility. However, it can also counteract the effect of λ (since it means that banking more today ends up increasing future requirements!). e.g. ifα = 1, the incentive to bank is completely cancelled out. But long-term imbalances sometimes more effectively controlled. Plot below uses current requirement schedule (very low compared to generation in model) withα = 0 (left) and α = 1 (right) SREC price (different vintage years) Month (from the start of EY2014) SREC price (different vintage years) Month (from the start of EY2014) Essen, Jan 15th 2014 p.35/38

67 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? Essen, Jan 15th 2014 p.36/38

68 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 Essen, Jan 15th 2014 p.36/38

69 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) Essen, Jan 15th 2014 p.36/38

70 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) Essen, Jan 15th 2014 p.36/38

71 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) Essen, Jan 15th 2014 p.36/38

72 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!) Essen, Jan 15th 2014 p.36/38

73 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! Essen, Jan 15th 2014 p.36/38

74 Further Work Needed Clearly very little research in this area so far, hence many possible topics to explore: Further calibration and testing on other US markets and also around the world if possible. Further investigation of market design alternatives. Incorporating the electricity market into the model: impacts of SREC prices on power and vice versa. Broader energy / environmental policy analysis: comparison with other subsidies for renewables, in terms of overall costs and benefits and price and quantity tradeoffs More mathematics: extending results in the direction of the carbon literature, for example through BSDE approaches Essen, Jan 15th 2014 p.37/38

75 Further Work Needed Clearly very little research in this area so far, hence many possible topics to explore: Further calibration and testing on other US markets and also around the world if possible. Further investigation of market design alternatives. Incorporating the electricity market into the model: impacts of SREC prices on power and vice versa. Broader energy / environmental policy analysis: comparison with other subsidies for renewables, in terms of overall costs and benefits and price and quantity tradeoffs More mathematics: extending results in the direction of the carbon literature, for example through BSDE approaches Essen, Jan 15th 2014 p.37/38

76 Further Work Needed Clearly very little research in this area so far, hence many possible topics to explore: Further calibration and testing on other US markets and also around the world if possible. Further investigation of market design alternatives. Incorporating the electricity market into the model: impacts of SREC prices on power and vice versa. Broader energy / environmental policy analysis: comparison with other subsidies for renewables, in terms of overall costs and benefits and price and quantity tradeoffs More mathematics: extending results in the direction of the carbon literature, for example through BSDE approaches Essen, Jan 15th 2014 p.37/38

77 Further Work Needed Clearly very little research in this area so far, hence many possible topics to explore: Further calibration and testing on other US markets and also around the world if possible. Further investigation of market design alternatives. Incorporating the electricity market into the model: impacts of SREC prices on power and vice versa. Broader energy / environmental policy analysis: comparison with other subsidies for renewables, in terms of overall costs and benefits and price and quantity tradeoffs More mathematics: extending results in the direction of the carbon literature, for example through BSDE approaches Essen, Jan 15th 2014 p.37/38

78 Further Work Needed Clearly very little research in this area so far, hence many possible topics to explore: Further calibration and testing on other US markets and also around the world if possible. Further investigation of market design alternatives. Incorporating the electricity market into the model: impacts of SREC prices on power and vice versa. Broader energy / environmental policy analysis: comparison with other subsidies for renewables, in terms of overall costs and benefits and price and quantity tradeoffs More mathematics: extending results in the direction of the carbon literature, for example through BSDE approaches Essen, Jan 15th 2014 p.37/38

79 References Our recent papers (available soon, or else by request): M. Coulon, J. Khazaei, W. Powell (2013) SMART-SREC: A stochastic model of the New Jersey solar renewable energy certificate market M. Coulon, J. Khazaei, W. Powell (2013) ADAPT: A Price-stabilizing Compliance Policy for Renewable Energy Certificates: The Case of SREC Markets Useful introductions (and market design discussions in the third): Bird, L., J. Heeter, and C. Kreycik (2011). Solar renewable energy certificate (SREC) markets: Status and trends Wiser, R., G. Barbose, and E. Holt (2011). Supporting solar power in renewables portfolio standards: Experience from the united states Felder, F. A. and C. J. Loxley (2012). The implications of a vertical demand curve in solar renewable portfolio standards Useful websites: Essen, Jan 15th 2014 p.38/38