Introduction Theory Data Results Conclusion
Option Returns, Risk Premiums, and Demand Pressure in Energy Markets
Kris Jacobs University of Houston
Bingxin Li West Virginia University
August 17, 2021
OptionReturns,RiskPremiums,andDemandPressureinEnergyMarkets:JacobsandLi 1/22 Introduction Theory Data Results Conclusion Background
Energy markets Increasing importance in financial markets Account for more than 70% of the S&P GSCI as of dollar weight Energy options are widely used in financial risk management A large literature in index and equity option returns; however, relatively few studies on energy option returns and risk premia Christoffersen and Pan (2019) Dew-Becker, Giglio, and Kelly (2019) Kang and Pan (2019) Prokopczuk, Symeonidis, and Simen (2017)
OptionReturns,RiskPremiums,andDemandPressureinEnergyMarkets:JacobsandLi 1/22 Introduction Theory Data Results Conclusion Objectives
Understand energy option returns as functions of maturity and moneyness, and across markets Returns on energy option strategies Delta-neutral portfolio, straddle, and zero-beta straddle Interpret these findings from the perspective of the existing theories, as well as the empirical results on index and equity option returns the variance risk premium the option traders’demand pressure
OptionReturns,RiskPremiums,andDemandPressureinEnergyMarkets:JacobsandLi 2/22 Introduction Theory Data Results Conclusion Theory
Coval and Shumway (2001, JF) Expected returns on calls are positive (higher than the risk-free rate) Expected returns on puts are negative (lower than the risk-free rate) Expected returns are increasing as a function of moneyness (K/F) These testable hypotheses are obtained for index option returns, assuming a "classical" pricing kernel that is monotonically decreasing in wealth
OptionReturns,RiskPremiums,andDemandPressureinEnergyMarkets:JacobsandLi 3/22 Introduction Theory Data Results Conclusion Theory
Bakshi and Kapadia (2003, RFS) Delta-hedged gains are zero in a Black-Scholes economy (with continuous rebalancing) With stochastic volatility, delta-hedged gains reflect the sign of the variance risk premium (the priced variance risk) These testable implications are for index option returns
OptionReturns,RiskPremiums,andDemandPressureinEnergyMarkets:JacobsandLi 4/22 Introduction Theory Data Results Conclusion Alternative Determinants of Return Patterns
Within a neoclassical framework: variance-dependent pricing kernels See Bakshi, Madan, and Panayotov (2010, JFE) and Christoffersen, Heston, and Jacobs (2013, RFS) Some success in explaining patterns in index option returns (Broadie, Chernov, and Johannes, 2009; Bondarenko, 2014) and crude oil options (Christoffersen and Pan, 2019) Demand-based option pricing See Bollen and Whaley (2004, JF), Gârleanu, Pedersen, Poteshman (2009, RFS) Net demand for different options by end-users puts pressure on prices In commodity (energy) markets, this comes down to hedging demand
OptionReturns,RiskPremiums,andDemandPressureinEnergyMarkets:JacobsandLi 5/22 Introduction Theory Data Results Conclusion Data
Four CME Energy Derivatives WTI crude oil futures and options (1990-2016) Henry Hub natural gas futures and options (1992-2016) Heating oil futures and options (1990-2016) RBOB gasoline futures and options (2004-2016) Maturities within a year: 1m, 2m, ..., 1y log(K /F ) Nine adjusted moneyness ( σ√τ ) intervals, [-2, 2], for each maturity
OptionReturns,RiskPremiums,andDemandPressureinEnergyMarkets:JacobsandLi 6/22 Introduction Theory Data Results Conclusion Futures Prices
Level (1m) Slope (1m • 1y)
) 150 20 l e r r
a 10 B
/ 100 $
( 0 l i
O 50 •10 e d u r •20 C 0 90 95 00 05 10 15 90 95 00 05 10 15 )
u 5 t 15 B m M / 10 $ ( 0 s a
G 5 l a r u t
a 0 •5 N 95 00 05 10 15 95 00 05 10 15
The natural gas market was in contango most of the time.
OptionReturns,RiskPremiums,andDemandPressureinEnergyMarkets:JacobsandLi 7/22 Introduction Theory Data Results Conclusion Implied Volatility of Futures Options
OTM Puts and Calls 0.8 0.8 s l a i 0.6 0.6 G O l e a r d u u t r
0.4 a 0.4 C N
0.2 0.2 0.85 0.9 0.95 1 1.05 1.1 0.85 0.9 0.95 1 1.05 1.1 0.8 0.8 1 Week l i
e 1Month
O 0.6
0.6 n i l
g 3Month o n i s t
a 6Month a e 0.4 G 0.4 H
0.2 0.2 0.85 0.9 0.95 1 1.05 1.1 0.85 0.9 0.95 1 1.05 1.1 Moneyness
Implied volatilities with shorter maturities are higher in all four markets for all moneyness. Implied volatilities in the natural gas market are higher than the other three markets.
OptionReturns,RiskPremiums,andDemandPressureinEnergyMarkets:JacobsandLi 8/22 Introduction Theory Data Results Conclusion Option Returns on Futures
Hold-to-maturity returns on futures options
call R = max(FT K, 0)/Ct,T 1, t,T − − put R = max(K FT , 0)/Pt,T 1, t,T − − where FT is the futures price at maturity T ; K is the strike price; Ct,T (Pt,T ) is the call (put) option price at time t with maturity.
OptionReturns,RiskPremiums,andDemandPressureinEnergyMarkets:JacobsandLi 9/22 Introduction Theory Data Results Conclusion Option Returns by Moneyness (1M)
Calls Puts ATM OTM OTM ATM [0, 0.2] (0.2, 0.65] (0.65, 1.1] (1.1, 1.55] (1.55, 2.0] Mean [•2.0, •1.55)[•1.55, •1.1)[•1.1, •0.65)[•0.65, •0.2) [•0.2, 0] Mean Panel A. Crude Oil •0.07 •0.14 •0.33 •0.56 •0.89 •0.47 •0.57 •0.36 •0.14 •0.01 0.01 •0.26 (0.89) (•1.69) (•3.21) (•4.92) (•13.68) (•7.90) (•2.51) (•2.13) (•1.02) (•0.10) (0.13) (•2.86) Panel B. Natural Gas 0.03 •0.11 •0.14 •0.52 •0.61 •0.26 •0.26 0.10 0.15 0.15 0.18 0.10 (0.21) (•0.84) (•0.85) (•3.16) (•2.39) (•2.68) (•0.88) (0.39) (1.05) (1.44) (1.87) (1.00) Panel C. Heating Oil 0.09 •0.06 •0.38 •0.70 •• •0.18 •• •0.61 •0.23 •0.16 •0.08 •0.19 (0.75) (•0.59) (•3.03) (•4.58) •• (•2.15) •• (•3.30) (•1.15) (•1.20) (•0.69) (•1.85) Panel D. Gasoline 0.10 •0.01 •0.47 •0.61 •• •0.22 •• •0.54 •0.19 •0.09 0.00 •0.17 (0.65) (•0.10) (•3.36) (•2.75) •• (•1.99) •• (•1.85) (•0.64) (•0.48) (•0.02) (•1.04)
Returns on OTM calls and puts are on average negative, except for natural gas put options. OTM call returns are lower (more negative) than put returns. Call (put) option returns in these three markets decrease (increase) in strike price.
OptionReturns,RiskPremiums,andDemandPressureinEnergyMarkets: JacobsandLi 10/22 Introduction Theory Data Results Conclusion Option Returns by Maturity
Crude Oil Natural Gas Heating Oil Gasoline Maturity Calls Puts Calls Puts Calls Puts Calls Puts 1m •0.47 •0.26 •0.26 0.10 •0.18 •0.19 •0.22 •0.17 (•7.90) (•2.86) (•2.68) (1.00) (•2.15) (•1.85) (•1.99) (•1.04) 2m •0.19 0.05 0.05 0.09 •0.09 •0.09 •0.12 •0.01 (•4.21) (0.83) (0.76) (1.75) (•2.16) (•1.30) (•2.05) (•0.08) 6m 0.04 0.16 0.03 0.03 0.03 0.09 0.01 0.10 (1.67) (3.50) (1.12) (1.06) (1.08) (1.44) (0.22) (0.80) 10m 0.06 0.08 0.01 0.07 0.04 •0.04 •• •• (2.54) (2.72) (0.32) (2.38) (1.21) (•1.53) •• •• Mean •0.22 •0.02 •0.07 0.08 •0.10 •0.09 •0.14 •0.07 (•10.81) (•0.71) (•2.08) (2.59) (•3.41) (•2.39) (•3.30) (•0.96)
Average short-maturity option returns are negative (except for the natural gas put options). Option returns increase in maturity and become positive at long maturities.
OptionReturns,RiskPremiums,andDemandPressureinEnergyMarkets: JacobsandLi 11/22 Introduction Theory Data Results Conclusion Average Option Returns (Crude Oil)
Crude Oil Calls Crude Oil Puts 0.5 0.5
0 0
1 1 Month •0.5 •0.5
•1 •1 •2 •1 0 1 2 •2 •1 0 1 2
2.5 2.5 90•16 2 2 90•04 05•08 1.5 1.5 09•16 1 1
6 6 Months 0.5 0.5 0 0
•2 •1 0 1 2 •2 •1 0 1 2 Adjusted Moneyness
Call (put) returns in a booming market is higher (lower). Average short-maturity (long-maturity) call returns decrease (increase) in strike price. Average put return patterns are opposite to call returns.
OptionReturns,RiskPremiums,andDemandPressureinEnergyMarkets: JacobsandLi 12/22 Introduction Theory Data Results Conclusion Findings in Energy Option Returns
Returns on OTM short-maturity options are negative, except for natural gas put options Average call returns are lower (more negative) than put returns at short maturities Short maturity put option returns increase with moneyness (K/F), while short maturity call option returns decrease with moneyness Option returns increase as a function of maturity, except for natural gas put options Average return patterns on natural gas market are different from the other three markets
OptionReturns,RiskPremiums,andDemandPressureinEnergyMarkets: JacobsandLi 13/22 Introduction Theory Data Results Conclusion Evidence from Other Option Markets
Index option returns show that average call returns exceed average put returns. Index option presents very large negative returns on OTM puts. That call (put) option returns decrease (increase) with strike prices is consitent with our findings (Broadie, Chernov, and Johannes, 2009; Bakshi, Madan, and Panyotov, 2010; etc.). U-shaped pricing kernels = moneyness pattern. ⇒
OptionReturns,RiskPremiums,andDemandPressureinEnergyMarkets: JacobsandLi 14/22 Introduction Theory Data Results Conclusion Delta-Hedged Returns
Following Bakshi and Kapadia (2003, RFS), the daily-rebalanced delta-hedged option gain for a call option over a period [t, T ] is
τ c c Πt, T = max(FT K, 0) Ct, T δt+n 1, T (Ft+n, T Ft+n 1, T ) − − − − − − n=1 τ X c rf (Ct, T δt+n 1, T Ft+n 1, T ). − − − − n=1 X Delta-hedged returns are defined as Delta-hedged gains are scaled by option prices for various adjusted moneyness intervals and maturities.
OptionReturns,RiskPremiums,andDemandPressureinEnergyMarkets: JacobsandLi 15/22 Introduction Theory Data Results Conclusion Delta-Hedged Returns
Crude Oil Natural Gas Heating Oil Gasoline Maturity Calls Puts Calls Puts Calls Puts Calls Puts 1m •0.19 •0.20 •0.02 •0.09 •0.06 •0.08 •0.13 •0.10 (•10.04) (•11.35) (•0.66) (•3.12) (•4.97) (•5.27) (•6.71) (•3.14) 2m •0.16 •0.16 0.04 •0.12 •0.07 •0.12 •0.11 •0.09 (•10.61) (•8.73) (1.51) (•7.58) (•5.50) (•8.15) (•6.19) (•3.05) 6m •0.02 •0.05 0.13 •0.09 •0.01 •0.09 •0.11 •0.03 (•1.17) (•2.24) (3.34) (•6.09) (•0.35) (•5.09) (•4.66) (•1.10) 10m 0.01 •0.05 0.13 •0.07 0.02 •0.09 •0.09 •0.05 (0.44) (•2.70) (3.60) (•4.36) (0.79) (•4.83) (•4.06) (•1.72) Mean •0.11 •0.12 0.05 •0.09 •0.04 •0.10 •0.12 •0.07 (•11.33) (•12.99) (2.91) (•8.81) (•5.65) (•12.05) (•10.88) (•4.56)
Delta-hedged returns are on average negative, except for NG calls at long maturities. Delta-hedged returns increase in maturity, although the pattern is relatively flat for NG, HO, and Gasoline. Delta-hedged put and call returns are similar in magnitudes.
OptionReturns,RiskPremiums,andDemandPressureinEnergyMarkets: JacobsandLi 16/22 Introduction Theory Data Results Conclusion Variance Risk Premium
P Q VRPt,T = Et [Vart T ] Et [Vart T ] → − → Variance Risk Premium (1 Month)
0.2 l i O e
d 0 u r C •0.2
90 95 00 05 10 15
0.2 s a G l a
r 0 u t a N •0.2
90 95 00 05 10 15
Natural gas variance risk premiums are more volatile.
OptionReturns,RiskPremiums,andDemandPressureinEnergyMarkets: JacobsandLi 17/22 Introduction Theory Data Results Conclusion Variance Risk Premium
Maturity 1m 2m 3m 4m 5m 6m Crude Oil •0.01 •0.02 •0.02 •0.02 •0.02 •0.02 (•4.97) (•4.80) (•3.99) (•3.15) (•3.04) (•3.37)
Natural Gas 0.00 •0.04 •0.05 •0.06 •0.06 •0.06 (•0.70) (•4.40) (•5.49) (•6.35) (•6.68) (•7.28)
Heating Oil 0.00 •0.02 •0.02 •0.02 •0.03 •0.02 (•6.58) (•4.86) (•5.09) (•4.25) (•4.22) (•2.76)
Gasoline •0.01 •0.01 •0.02 •0.02 •0.01 •0.02 (•1.78) (•1.01) (•1.42) (•0.97) (•0.70) (•1.07) Variance Risk Premiums are on average negative. NG variance risk premiums are much lower.
OptionReturns,RiskPremiums,andDemandPressureinEnergyMarkets: JacobsandLi 18/22 Introduction Theory Data Results Conclusion Variance Risk Premium
Bakshi and Kapadia (2003, RFS): If volatility risk is priced in a stochastic volatility model, a negative VRP implies that the expected delta-hedged gains are negative. A negative VRP implies that option returns are inversely related to variance = maturity pattern. ⇒
OptionReturns,RiskPremiums,andDemandPressureinEnergyMarkets: JacobsandLi 19/22 Introduction Theory Data Results Conclusion Traders’Position and Net Demand Pressure
Panel A. Crude Oil 104 104
s 5 5 l a i s l c a r i e c r m 0 e 0 m m o c m • o n C o
N •5 •5
1995 2000 2005 2010 2015 2020 1995 2000 2005 2010 2015 2020 Panel B. Natural Gas 105 105 1 .5 1 .5 1 1 s l a i s l c a r 0 .5 0 .5 i e c r m 0 e 0 m m o c m • •0 .5 o •0 .5 n C o
N •1 •1 •1 .5 •1 .5 1995 2000 2005 2010 2015 2020 1995 2000 2005 2010 2015 2020
Traders’position from CFTC COT F and F&O reports. Commercial are net short on average. Inbalances are the largest in the crude oil market.
OptionReturns,RiskPremiums,andDemandPressureinEnergyMarkets: JacobsandLi 20/22 Introduction Theory Data Results Conclusion Traders’Position and Net Demand Pressure
Panel A. Crude oil ATM Put Delta•hedged Delta•hedged Non• Ret Call Ret Put Ret Commercials Commercials ATM Call Ret •0.51 0.24 0.15 •0.17 0.18 ATM Put Ret 1.00 0.25 0.33 •0.02 0.00 Delta•hedged Call Ret 1.00 0.94 •0.26 0.26 Delta•hedged Put Ret 1.00 0.03 •0.03 Panel B. Natural gas ATM Call Ret •0.46 0.03 0.01 •0.17 0.17 ATM Put Ret 1.00 0.09 0.11 0.06 •0.07 Delta•hedged Call Ret 1.00 0.97 •0.07 0.07 Delta•hedged Put Ret 1.00 0.04 •0.05
Call (put) option returns and delta-hedged call (put) returns are negatively correlated with non-commercial (commercial) option traders’positions. The larger the net positive position of the non-commercials (speculators), the lower (more negative) the call option return.
OptionReturns,RiskPremiums,andDemandPressureinEnergyMarkets: JacobsandLi 21/22 Introduction Theory Data Results Conclusion Conclusion
Short-term put (call) option returns increase (decrease) as a function of the strike price. OTM call returns are more negative than OTM put returns. Delta-hedged returns, ATM straddle returns, and zero-beta straddle returns are negative at short maturities but become positive at long maturities. Our estimates of variance risk premium explain part of the return partterns in maturity. Option traders’positions may effect option returns in these markets.
OptionReturns,RiskPremiums,andDemandPressureinEnergyMarkets: JacobsandLi 22/22