SwissQuote Conference EPFL Lausanne, Switzerland

1 November 2013

Extracting Higher Value from Physical Assets

Mahmoud Hamada, PhD, MBA Agenda

► Time Commodity Trading ► Location Section1 Optionality ► Quality ► Lot Size

Power Plant as a ► Motivating Example Real Option Section2

► Optimal Control Gas Storage ► Rolling Intrinsic Optimization Section3 ► Basket of Spread Options ► Comparison

Concluding Remarks ► Towards a robust approach Section4 ► Asset-backed trading in worldwide integrated business

1 November 2013 Page 2 Swissquote Conference – Mahmoud Hamada Monetizing real optionality through interconnected set of logistical assets

Location: Procure Fuel oil from US refinery and sell forward three months on Asian benchmark

Time: Store Fuel oil for two months until price increases

Quality: Blend with cutter stock in tank to marine fuel specs

Diversion option

Lot: Take bunker fuel in smaller ship to Singapore

1 November 2013 Page 3 Swissquote Conference – Mahmoud Hamada Power plant as a real option – motivating example

Gas 1 Electricity

Price (€/푴풘풉): 푷푮

Tariff (€/푴풘풉): X

Price (€/푴풘풉): 푷푬 2 ► If V is variable cost of running the plant, then Electricity 1. If 푷푬 − 푯푹 × 푷푮 − 푽 ≥ ퟎ, Run the plant.

2. If 푷푬 − 푯푹 × 푷푮 − 푽 ≤ ퟎ, Do NOT run 1 ► Plant’s P&L: 횷ퟏ = 푿 − 푯푹 × 푷푮(€/푴푾풉) ► The operational margins from running the plant 2 following this strategy as ► Plant’s P&L: 횷ퟐ = 푿 − 푷푬(€/푴푾풉) ► The difference between the two 횷 = 풎풂풙 {푷푬 − 푯푹 × 푷푮 − 푽, ퟎ} strategies equals the spark spread: ► This is payoff of the on the spread 횷 − 횷 = 푷 − 푯푹 × 푷 (€/푴푾풉) between power and fuel with the variable cost ퟏ ퟐ 푬 푮 being the strike.

1 November 2013 Page 4 Swissquote Conference – Mahmoud Hamada Gas storage – a profitable real option

► Storage facilities are time machines that let the operator move production capacity from one point in time to a later one. ► This mechanism enables smoothing of the supply response to demand fluctuations. Type Working gas Cushion gas Injection Withdr. Operation capacity period period Depleted field  300 mcm  50% (already 150 - 250 days 50 - 150 days Seasonal

present) Underground

Aquifer  300 mcm Up to 80% 150 - 250 days 50 - 150 days Seasonal

Salt cavern  150 mcm  25% 20 - 40 days 10 - 20 days Peak shaving, balancing

LNG tank  500.000 m3 none 1 - 2 days 1 - 10 days Short term 1 Compression /600 balancing

Surface Gaso-meter  50.000 m3 none 1 - 2 days 1 - 2 days Daily / weekly balancing

Line pack varying none ≤ 1 day ≤ 1 day Intraday balancing

1 November 2013 Page 5 Swissquote Conference – Mahmoud Hamada Three main approaches to gas storage valuation

Approach Characteristics

Optimal Control ► Rigourous mathematical formulation of the poblem. ► Stochastic Dynamic Programming (SDP) ► Least Squares Monte Carlo (LSMC) ► Solving Stochastic Differential Equations (SDE)

Rolling Intrinsic ► Most transparent and intuitive methodology ► Flexibility value is managed by locking-in observable forward curve spreads and then making (risk-free) adjustments to hedge positions as prices move, in order to monetise market

Calendar Spread ► Considers a storage contract as a series of time spread options Options to gas from one period to another in the future ► The volume of available spread options is constrained by the physical characteristics

1 November 2013 Page 6 Swissquote Conference – Mahmoud Hamada Solving the optimal control

푇 ► 푆= current price per unit of ∗ −푟(휏−푡0) 푉 푡0, 푆, 퐼 푡0 = max 피푡 푒 푐 − 푎 퐼, 푐 푆푑휏 (1) natural gas. 푐(푆,퐼,푡) 0 푡0 ► 퐼 = current amount of working 푐푚푖푛(퐼) ≤ 푐 ≤ 푐푚푎푥(퐼) (2) gas inventory. 푑퐼 = −(푐 + 푎(퐼, 푐))푑푡 (3) ► 푐 = amount of gas currently being released from (c > 0) or 푁 injected into (c < 0) storage. 푑푆 = 휇(푆, 푡)푑푡 + 휎(푆, 푡)푑푊 + 훾 S, t, 퐽 푑푞 (4) 푘 푘 푘 ► 퐼푚푎푥 = maximum storage 푘=1 capacity.

► 푐푚푎푥(퐼) = maximum 1 푤𝑖푡ℎ 푝푟표푏푎푏푙𝑖푡푦 휆푘(푆, 푡)푑푡 (5) deliverability rate 푑푞푘 = 0 푤𝑖푡ℎ 푝푟표푏푎푏푙𝑖푡푦 (1 − 휆푘(푆, 푡)푑푡) ► 푐푚푖푛(퐼)= maximum injection rate ► 푎(퐼, 퐶)= amount of gas lost 푉 푡, 푆, 퐼 = given c units of gas being 푡+푑푡 released or injected into storage. ∗ −푟(휏−푡) max 피푡 푒 푐 − 푎 퐼, 푐 푆푑휏 + 푉(푡 + 푑푡, 푆 + 푑푆, 퐼 + 푑퐼) 푐(푆,퐼,푡) 푡

1 November 2013 Page 7 Swissquote Conference – Mahmoud Hamada Least Square Monte Carlo

풏 풏 풏 1.Simulate N independent price paths 푺ퟏ, 푺ퟐ,…, 푺푻, 풏 = ퟏ, … , 푵 2.Carry out backward induction: For 풕 = 푻, … , ퟏ For each simulation n = 1, …, N 풎 For each storage level 푰풕 퐦 = ퟏ, … 퐌 Solve the one stage problem and find a decision rule, 풏 풏 −풓풕 풏 푽풕 = 퐦퐚퐱 풄 − 풂 풄 푺풕 + 풆 푬 푽풕+ퟏ¦퓕풕 풄 subject to: storage physical constraints Next Next ► Longstaff and Schwartz (2001) Next 2 푉푡+1 = 훾0 + 훾1푆푡 + 훾2푆푡 + 휀푡

For n=1, …, N Compute the present value of the storage by summing the discounted future cash flows following the decision rule Next 4.Storage value is the average of the present values under n paths

1 November 2013 Page 8 Swissquote Conference – Mahmoud Hamada Rolling Intrinsic April 1st

€ / MWh long short 35

30

25

20

15 locked 10 spread

5

Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr

Net Position P&L Market Value

+ long Jul at 15 0 - short Dec at 30

= short highest spread € 15 / MWh € 15 / MWh

1 November 2013 Page 9 Swissquote Conference – Mahmoud Hamada Rolling Intrinsic April 2nd

€ / MWh closelong short 35

30

25

20

15 loss locked 10 spread

5

Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr

Net Position P&L Market Value + long Jul at 15 loss of € 2.5 / MWh - short Jul at 12.5 + long Aug at 10 - short Dec at 30

= short highest calendar spread € 20 / MWh - €2.5/MWh €20/MWh

1 November 2013 Page 10 Swissquote Conference – Mahmoud Hamada Rolling Intrinsic April 8th

long closelong closeshort short € / MWh 50% 50% 50% 50%

35 locked 30 spread loss 2 25

20

15

10 Δ locked 5 spread1

Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr Net Position P&L Market Value

+ long50% Jun at 10 + long50% Aug at 10 profit of € 2.5 / MWh - short50% Feb at 35 - short2 Aug at 12.5

- short50% Dec at 30 loss of € 3 / MWh + long50% Dec at 27

= short highest spread (at 25) for 50% of capacity - € 0.5 / MWh € 19.75/MWh + short highest spread (at 14.5) for 50% of capacity

1 November 2013 Page 11 Swissquote Conference – Mahmoud Hamada Valuation using the rolling intrinsic approach

► This is the most transparent and intuitive methodology and thus is often favoured by asset managers and traders. 1. We enter into the forward positions suggested by the optimal injection/withdrawal schedule for this forward curve. 2. If the forward changes favourably, we readjust our positions to capture the positive difference. If the curve moves in an unfavourable way, we do nothing. ► A simulation based methodology can be implemented based on the following logic: ► t = 0: Optimise the storage facility against the currently observed forward curve and execute hedges to lock in intrinsic value. ► t = 1 to T: Simulate the movement in the forward curve and re-optimise storage contract. ► Calculate the value of unwinding existing hedges and placing on new hedges against re-optimised profile and execute profitable hedge adjustments. ► At any point in time the hedge position matches the planned injection and withdrawal profile and the outturn will always be higher than the initial intrinsic hedge as adjustments are only made if it is profitable to do so

1 November 2013 Page 12 Swissquote Conference – Mahmoud Hamada Valuation of Gas Storage using basket of Calendar Spread Options

Futures prices pc/th

50

Spread = 10 40

th Feb. 15 30

20

10

Trader Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb

Sell Calendar Spread option:

Payoff max(FFeb – FNov, 0) Expiry October 31st Intrinsic Value 10 pc/th Total Value = 17pc/th Time Value 7 pc/th

1 November 2013 Page 13 Swissquote Conference – Mahmoud Hamada Valuation of Gas Storage using basket of Calendar Spread

Options = =

50 Spread

- 15 40 ► The option is worthless 30 ► Trader keeps the premium. 20

Oct Nov Dec Jan Feb ► Option exercised Spread decreasing ► Spread option loss = 25p/th Oct. 31st ► However, the availability of storage allows him to buy Futures October gas at 25p/th and short prices forward the Feb. at 50p/th (pc/th)

50 Spread ► He stores the Oct. gas, keep it until 1st Feb, and sells it using Trader 40

= = Feb. contract at 50p/th. 2

30 5 ► From this position Trader’s profit= 25p/th. 20 ► Trader’s net position is: -25p/th 10 (CS option loss) + 25p/th (storage and futures spread) + Oct Nov Dec Jan Feb 17p/th (CS option premium) = Spread increasing 17p/th (the premium).

1 November 2013 Page 14 Swissquote Conference – Mahmoud Hamada Concluding Remarks

► The example of storage shows the complexity of the optimizing a physical asset ► Taking a macro view, can we optimize the portfolio of power plants, gas storage, pipeline capacity, shipping .. for a large scale commodity trading?

1 November 2013 Page 15 Swissquote Conference – Mahmoud Hamada Thank You!

1 November 2013 Page 16 Swissquote Conference – Mahmoud Hamada