Real Options & Complex Energy Contracts Fabio Cannizzo Head, Quantitative Finance Centre BP, Integrated Supply & Trading cannf1@bp.com
Quantitative Finance Centre Integrated Supply & Trading (IST) centralises all BP trading and planning activities with the goal of: Optimising supply & Trading Providing Risk management solution to external and internal clients Taking proprietary positions The QFC is a team of twelve quantitative analysts providing with quantitative support to all IST operations. Team s diverse and comprehensive expertise embraces a wide range of areas, as derivatives, structured products, econometrics and real options The aim of the group is to carry out extensive research and find tailored solutions in order to maximise the trading profit and reduce the risk of holding positions
IST Risk Management role Within IST, bpriskmanager works in close collaboration with QFC with internal and external customers with the goal of: offering Energy risk management solutions helping clients in analysing their risk, markets and potential hedging tools designing structured solutions tailored to specific customers requirements
Real Options & Complex Contracts In the Energy Industry we often deal with complex portfolios of derivatives, in many different forms Real options Options embedded in physical contracts Exercise strategy of assets Flexibility in operations Complex pricing formulas Embedding Options Embedding Quanto risk Based on illiquid indexes Etc
Real Options & Complex Contracts 2 Often these portfolios are not valued properly, neither treated appropriately from a Risk Management point of view An integrated correct financial analysis can: decompose these portfolios into positions correlate them with liquid measures provide with the right sensitivities to market risk factors Both Risk Management and Trading practices would benefit from a correct analysis, which leads to: a better understanding of whole exposure more effective hedging and trading decisions
Option to Change Bill of Lading of a Ship Some long term oil supply contracts assumes that the volume of oil paid in a certain period is nominated in advance ( marketable volume ) Each marketable volume is priced at the average of the spot prices on the lifting dates, weighted by the actual amount of oil loaded in the period Consequently, a cargo placed on the last day of a period or on the first day of the following periods, can significantly change the price Since we can often have the flexibility to change the bill of lading of 1 or 2 days, we own a complex type of calendar spread option
Option to Change Bill of Lading of a ship 2 This results in an exposure to the Oil Forward curve Obviously whoever who has this contract in his book would exercise when it is in the money But if we limit ourselves to that, we give away the time value of the option, which we could instead try to lock in via a deltahedging strategy In conclusion, we could make more money! Brent 120 80 40 0-40 -80 Equivalent Long/Short Week
Other Examples of Physical Contracts Almost all energy contracts/assets embed optionality Some of them embed a huge optionality! Some examples Take Or Pay flexibility Pay something at the min of { } Flexibility to supply a customer from a hub or another Flexibility to choose when to deliver / receive Flexibility to chose where to deliver / receive Switch fuel Switch feedstock Switch product This is far to be an exhaustive list!
An Example of Flexibility in Operations An LNG producer can ship LNG to Europe and sell at NBP in Pounds (base case) or ship to the US, incurring extra transportation costs H, and sell at HH in Dollars Incremental value is a spread option: max[hh*x /$ -NBP-H; 0] This option makes the producer long HH and short NBP This combines with the basic exposure to NBP (long) and reduces it An additional complication: if decision is taken to ship to US additional shipping capacity needs to be booked, which force to stick to the decision for at least 3 months This gives to these set of options a compounding nature
Gas Storage Contracts Owning a Gas Storage contract (or device) allows to: Buy gas when it is cheap, also if not immediately needed Store it Use it at a later time, when buying it on the market would be expensive If we are long Gas Storage, we can: Inject gas up to some specified max injection rates (e.g. from 0 to 30,000 th/day), incurring injection costs Withdraw gas up to some specified withdrawal rates (e.g. from 0 to 100,000 th.day), incurring withdrawal costs Our storage has some maximum capacity
Gas Storage Contracts 2 We have to take decisions (exercise options) continuously: at any given time during the term of the contract, given the level of price of Gas, and our inventory level, we need to decide what to do in order to exploit the asset as best as possible withdraw max Immediate cash flow Expectation of future value W t *(S t -Wc t ) + E t [t,s t+1,v t -W t ] t, S t,v t? max do nothing 0 + E t [S t+1,v t ] inject max I t *(-S t -Ic t ) + E t [t,s t+1,v t+ I t ]
Gas Storage Contracts 3 All these decisions make a complex portfolio of highly compounded options! All these options are interdependent over time, i.e. our action today impacts the flexibility we have tomorrow We need an appropriate valuation model in order to: Value our position Calculate the Greeks of our position Incorporate our position into our MVar system Trade around it Support our exercise decisions
Illiquid indexes example Rheinschiene In Germany lots of contracts are indexed to Rheinschiene quotes for FO and GO Rheinschiene quotes (in ) are numbers published monthly by a statistical agency on mandate of the government, which are supposed to track the fair price of GO and FO over the relevant month in the Rheine area Rheinschiene index is not a traded security, but it is possible to identify a liquid proxy for it as a particular combination of historical prices of a basket of other liquid commodities and currencies
Illiquid indexes example Rheinschiene 2 Index Predictor Residual 250.000 10.0 200.000 5.0 150.000 0.0 100.000-5.0 50.000-10.0 0.000-15.0 07/1998 02/1999 08/1999 03/2000 10/2000 04/2001 11/2001 05/2002 BP is in the position to manage this risk (including the basis risk), and to offer consumers exposed to Rheinschiene index swaps (fixed for Rheinschiene)
Quanto Risk How often do you see pricing formulas like: P( ) = α + β ( GO($) / GO 0 ($) )? These formula embeds hidden risks and potentially some value They need to be analysed properly We show for example how currency risk kicks in
Quanto Risk - Example A long term supply contract bind us to buy 1000 th of Gas in Dec at: P(c ) = P 0 (c /th) ( GO($/t) / GO 0 ($/t) ), where, P 0 = 16 c /th and GO 0 = 200 $/t. Aggregating the constants, we can say we ll pay: P(c ) = 0.08 GO($/t) Today s forward price of GO for Dec is 210 $/t, which would result into us paying: 1000x0.08x210=16,800 c We wish to lock in today the value of this liability and we think we could do that take taking a position in Dec GO Therefore we buy 0.08x1000=80 t of Dec GO for 210 $/t, and we relax: job done!
Quanto Risk Example 2 What happen then in December? If the price of GO turns out to be exactly 210 $/t, then the P&L of the GO hedge is zero, and the price paid for gas is exactly 16,800 c. Great! If the price of GO is different from 210 $/t, say 220 $/t, then the hedge has a profit of 10x80=800 $, while the price paid for gas is 1000x0.08x220=20,000 c. Does the hedge (in $) offset exactly the different price? Our net position is: 800 $ - 20,000 c which in general is not equal to 16,800 c! Effectiveness of the hedge depends from the spot FX rate at which I will be able to convert in Euro the P&L of the hedge We cannot even lock in this exchange rate in advance and keep it into account when defining the volume of the hedge, because we don t know the P&L of the hedge in advance! A static hedge cannot make the job!
The Spanish Gas Formula - Introduction Spanish authority decides to change pricing formula in March 2002 Most gas contracts in Spain are indexed on this formula New formula is dependent on historical prices of a basket of oil products, with coefficients non-constant, but dependent on Brent prices! Analysing the formula, we will find a complex portfolio of options
The Spanish Gas Formula - Description A linear combination of X-factors, translated into Euros, with coefficients Kj and Cj,i dependent on Brent price Price = K K K K 1 2 3 4 + + + + 7 i = 1 7 i= 1 7 i= 1 7 i= 1 C C C C 1, i 2, i 3, i 4, i X i X X X FX i i i FX FX FX / $ / $, / $ / $,,, if Brent 17 if 17 < Brent < 20 if 20 Brent 26.5 if Brent > 26.5 K j C j,1 C j,2 C j,3 C j,4 C j,5 C j,6 C j,7 Brent <= 17 0.333761 0.011754 0.000927 0.000422 0.001103 0.000376 0.00024 0.000288 17 < Brent < 20 0.586805 0.011754 0.000089 0.000422 0.000076 0.000376 0.000076 0.000288 20 <= Brent <= 26.5 0.085958 0.011754 0.001424 0.000422 0.001226 0.000376 0.001226 0.000288 Brent > 26.5 0.569829 0.011754 0.000508 0.000422 0.00061 0.000376 0.000006 0.000288
The Spanish Gas Formula Description 2 X i variables are the average of monthly averages price of certain commodities over the two preceding quarters (this values are updated on a quarterly basis). In particular: o X 1 is the price FOB of Arabian Light o X 2 is the price CIF of Gasoil 0.2% at Genova-Lavera market o X 3 is the price CIF of Gasoil 0.2% at ARA market o X 4 is the price CIF of Fuel Oil 1% at Genova-Lavera market o X 5 is the price CIF of Fuel Oil 1% at ARA market o X 6 is the price CIF of Fuel Oil 3.5% at Genova-Lavera market o X 7 is the price CIF of Fuel Oil 3.5% at ARA market o Brent variable is the average of monthly averages price of Brent Dated over the two preceding quarters o FX /$ is the average exchange rate over the preceding month, calculated on the basis of daily quotes. This value is updated on a monthly basis.
The Spanish Gas Formula Analysis Decomposition of the pricing formula in two portions respectively independent and dependent on Brent DTD price First we strip out the common components: Basic exposure K j C j,1 C j,2 C j,3 C j,4 C j,5 C j,6 C j,7 Indep. on Brent 0.085958 0.011754 0.000089 0.000422 0.000076 0.000376 0.000006 0.000288 Conditional exposure K j C j,1 C j,2 C j,3 C j,4 C j,5 C j,6 C j,7 Brent <= 17 0.247803 0 0.000838 0 0.001027 0 0.000234 0 17 < Brent < 20 0.500847 0 0 0 0 0 0.00007 0 20 <= Brent <= 26.5 0 0 0.001335 0 0.00115 0 0.00122 0 Brent > 26.5 0.483871 0 0.000419 0 0.000534 0 0 0 Which we value as a commodity swap guaranteed in Euro
The Spanish Gas Formula Analysis 2 We are left with a portfolio of pure options Let s look for example at the K coefficient alone. If we forget for a moment the FX conversion rate, we can say we own a portfolio of Asian Binary options! K j Brent <= 17 0.247803 17 < Brent < 20 0.500847 20 <= Brent <= 26.5 0 Brent > 26.5 0.483871 long 0.483871 binary Call @ 26.5 $/barrel long 0.470847 binary Put @ 20 $/barrel short (0.470847-0.247803) binary Put @ 17 $/barrel Revenues [c$/mwh] 0.6 0.5 0.4 0.3 0.2 0.1 0-0.1 Unitary revenues at maturity 0 5 10 15 20 25 30 35 Brent dated avg. price [$/barrel]
The Spanish Gas Formula Analysis 3 If we now consider also the FX then we can say that the cash flow delivered from these binary options struck on Brent is dependent on the average of the exchange rate If we consider the other pieces of the formula, where the price of a commodity is involved, we can say that the cash flow delivered from these binary options struck on Brent is dependent on the average of the exchange rate times the price of another commodity In practice, we have a portfolio of options of the type: if (Avg Y) is greater than K, then receive (Avg X * Avg FX)
The Spanish Gas Formula Analysis 4 Behaviour of GetXConditionalToY option: Premium Asset X 160 80 0 1 5.35 9.7 14.05 18.4 22.75 27.1 Asset Y 200 180 160 140 120 100 80 60 40 20 0 grows non-linearly with both X and Y
The Spanish Gas Formula - Review Willing or not, if we sell gas to Spanish customers, we are automatically long a bizarre portfolio of weird options. What do we want to do with it? We need to be aware of that! We want to understand our position, possibly to trade around it We want to understand what is our total exposure (MVar), in order to take an informed decision if to hedge or not If we buy and hedge from a third party, we want to be aware of how much it costs to us An appropriate analysis can support all these decisions
The message Embedded derivatives are the norm in Energy A great source of value and a very dangerous tool at the same time If we are exposed to derivatives products, we need to be aware of it If they work in our favour (long optionality) and we want to exploit them, we should do it as best as we can. This in general does not reduce to exercise when in-the-money We need to understand how they can hurt us, and what we can do to protect ourselves We need to understand clearly our total position Trading and hedging decisions need to be supported by a solid financial analysis