Valuation and Trading of Natural Gas Storage Assets

Valuation and Trading of Natural Gas Storage Assets

Dr Lionel GreeneNon-Linear Derivatives Trading

24th Sep 2012

Contents

• Purpose of Storage• Sources of Value• Modelling Requirements• Mathematical Framework• Available Methods• Hedging Instruments• Simulation of Different Types of Storage Products• Typical Storage Usage• Average Flows• Trading: Re-hedging after Exercise• Market vs. Model Risk• Dynamic Risk Management• Conclusion

Purpose of Storage in the Natural Gas Market

• Allows the holder to capitalise on cash-and-carry arbitrage opportunities in the markets.

• These opportunities exist because the volume of storage available to the market is not sufficient to neutralise transient fluctuations in demand.

• Types of storage contracts:1. Physical : these range from

very-short-cycle (filled and emptied in a few days) to seasonal products. Widely used across Europe.

2. Virtual : these contracts provide “storage” of PHYSICAL gas. Value is extracted by CALLing previously “stored” gas for sale into the spot market or from PUTting gas into storage for forward delivery.

Sources of Value for Natural Gas Storage

• All value comes from the opportunity to trade time-spreads

• Many different time-scales are of interest:– Short term (<1 day – 2 weeks)– Medium term (2 weeks – 2 months)– Long term (2 months – 1 year)

• Spreads of interest:– Prompt : within-day or day-ahead vs. periods up to ~2 weeks

out– Weekend vs. weekday prices– Spreads between forward months (within the same season)– Spreads between seasons

• Some “real” arbitrage is possible where both legs of the time spread being captured are liquid, however it is often necessary to depend on “statistical” arbitrage and thus TRADING STORAGE PRODUCTS INVOLVES UNHEDGABLE RISKS

Modelling Requirements

Storage model

INPUTS OUTPUTSMarket (liquid) parameters :Forward curvesImplied volatilities

Estimated (illiquid) parameters :CorrelationsSpike frequencies

Spot trading position(injection or withdrawal)

Forward trading position(deltas and other “Greeks”)

Mathematical Framework

• Pricing is consistent with the hedged portfolio approach for contingent claims pricing as developed by Black-Scholes(1971)/Merton(1973) based on the following assumptions:

• The application of the expectation hypothesis in a risk-neutral universe

• Under the assumptions of continuous trading• Availability of traded assets (such as Swaps, Swaptions,

etc.) with sufficient liquidity and depth• Frictionless markets• The imposition of arbitrage-free valuation constraints • Lognormal diffusion process with spikes • Deterministic discount functions • Ito’s calculus

Available Methods: Pros & Cons

• Finite difference: provides exact solution for simple price models. Can be prohibitively slow for more complex, multi-factor price-diffusion models

• Trees: similar to finite difference but may require a larger computational domain for similar results

• Stochastic Dynamic Programming: only effective for very simple price diffusion models, the danger is that the price-diffusion process is chosen to fit the model (optimisation)

• Least Squares Monte Carlo: can deal with an arbitrary level of complexity in terms of price simulation but requires more research in order to improve stability and convergence of the “Greeks” (this method may ultimately provide an excellent framework but computational power is still an issue)

Hedging Instruments

• Physical/financial swaps for hedging Delta– Intra-month products (Within-day, Day-ahead, Balance-

of-week, week-ahead, weekends)– Month products, Quarterly products, Seasonal products

• Daily options, Monthly options, Swing options for hedging Gamma, Vega, Theta

Simulation of Different Types of Storage Products

• Two cases considered:

– Short cycle storage (e.g. 10 days to fill, 10 days to empty)

– Seasonal storage (e.g. 180 days to fill, 60 days to empty)

• The following two graphs show typical single realisations of a simulated year of operation

• The principal difference between the two realisations is the number of reversals of flow: this indicates which factors dominate the valuation and thus also indicate where most care has to be taken with the individual valuations (e.g. poor estimation or hedging of winter-summer spreads may have little impact on the trading of short-cycle storage products)

Typical Storage Usage: 1 short-cycle product

Typical single run for short-cycle storage

0

2

4

6

8

10

12

14

16

1-Oc

t15-Oct

29-Oct

12-Nov

26-Nov

10-Dec

24-Dec

7-Jan

21-Jan

4-Feb

18-Feb

4-Mar

18-Mar

1-Ap

r15-Apr

29-Apr

13-May

27-May

10-Jun

24-Jun

8-Jul

22-Jul

5-Au

g19-Aug

2-Se

p16-Sep

30-Sep

Volume in store

0

20

4060

80

100

120140

160

180

Gas price [p/th]

Volum e in storeForward curve at startSim ulated curve

Typical Storage Usage: 2 seasonal product

Typical single run for seasonal storage

0

10

20

30

40

50

60

70

1-Oc

t15-Oct

29-Oct

12-Nov

26-Nov

10-Dec

24-Dec

7-Jan

21-Jan

4-Feb

18-Feb

4-Mar

18-Mar

1-Ap

r15-Apr

29-Apr

13-May

27-May

10-Jun

24-Jun

8-Jul

22-Jul

5-Au

g19-Aug

2-Se

p16-Sep

30-Sep

Volume in store

0

2040

60

80100

120

140160

180

Gas price [p/th]

Volum e in storeForward curve at startSim ulated curve

Average Flows for Short-Cycle Storage

• It is difficult to observe the effect of weekday-weekend spreads for a single realisation of a short-cycle storage product, however, the average flows (from 1000 simulations) clearly shows the effect of the assumptions embedded in the initial forward curve used for the valuation

Typical volum e in store short-cycle storage

0

2

4

6

8

10

1-Oc

t15-Oct

29-Oct

12-Nov

26-Nov

10-Dec

24-Dec

7-Jan

21-Jan

4-Feb

18-Feb

4-Mar

18-Mar

1-Ap

r15-Apr

29-Apr

13-May

27-May

10-Jun

24-Jun

8-Jul

22-Jul

5-Au

g19-Aug

2-Se

p16-Sep

30-Sep

Volume in store

0102030405060708090100

Gas price [p/th]

Volum e in storeForward curve at start

Trading: Re-Hedging After Exercise

• Example shows the impact on the forward positions of injection or withdrawal

• The re-distributed volume is not associated with a specific period, it is “smeared” over the entire forward curve (for seasonal storage products the effect is more pronounced)

• Effectively hedging these, constantly changing, forward positions is associated with a significant portion of the value of the asset

• Hedging the second order effects can NOT be achieved using the instruments currently available in the market: trading storage is RISKY

Expected volum e in store D-1

0

1

2

3

4

5

6

7

8

9

15-Feb

18-Feb

21-Feb

24-Feb

27-Feb

2-Mar

5-Mar

8-Mar

11-Mar

14-Mar

17-Mar

20-Mar

23-Mar

26-Mar

29-Mar

Change to forw ard position caused by w ithdraw ing 1 unit

-1-0.9-0.8-0.7-0.6-0.5-0.4-0.3-0.2-0.10

15-Feb

18-Feb

21-Feb

24-Feb

27-Feb

2-Mar

5-Mar

8-Mar

11-Mar

14-Mar

17-Mar

20-Mar

23-Mar

26-Mar

29-Mar

Change to forw ard position caused by injecting 5 units

0.0

0.5

1.0

1.5

2.0

2.5

3.0

15-Feb

18-Feb

21-Feb

24-Feb

27-Feb

2-Mar

5-Mar

8-Mar

11-Mar

14-Mar

17-Mar

20-Mar

23-Mar

26-Mar

29-Mar

Market vs. Model Risk: Effect of Spot Volatility

• Currently European gas markets exhibit very low liquidity for products with large spot-volatility risks

• Parameter estimation, in particular spot-volatility, may be a much more significant factor in the pricing of storage products than model risks

• In this situation the focus should remain on market modelling

Effect of spot volatility

15,000

17,000

19,000

21,000

23,000

25,000

27,000

29,000

50% 100% 150% 200% 250% 300% 350%Spot volatility param eter

SBU value [£]

NBP SAP volatilities

100%

150%

200%

250%

300%

350%

400%

Jun-00

Oct-0

1

Feb-03

Jul-04

Nov-05

1 year rolling volatility6 m onth rolling volatility

Dynamic Risk Management

• Classic delta hedging is not possible• Transaction and liquidity costs are high• Be acutely aware of the limitations of dynamic hedging

• You always have a position, it’s only the size that is in question

• Advocate active hedging rather than passive hedging i.e. anticipate(be a trader) rather than react(not a quant)

• Use proprietary trading techniques to risk manage net positions

• Gaps arise from imperfect synchronisation between buyers and sellers

• Wait for liquidity pockets to adjust positions• Managing risks in illiquid markets is a craft and not a

science

Conclusion

• Quantitative modelling techniques can be used to provide a framework for the valuation and trading of storage assets

• Dynamic hedging is necessary to reduce the risk associated with storage trading, however, many elements (correlation between forward markets, weekend-weekday spreads, spot volatility etc.) can NOT be hedged in the current market

• Model risk can be small compared with un-hedgable market risk: expert judgement in choosing appropriate modelling assumptions will determine valuation for storage and all other ILLIQUID exotics; FAIR VALUE does not exist