Groves

Commodity Hybrids Trading

James Groves, Barclays Capital

What is hybrids trading?

• Multi-asset commodity payoffs• Who wants to trade these?• Customer base• Investors (retail, institutional)• Hedge Funds• Corporates

Growth of hybrid derivatives

-

1,000,000,000

2,000,000,000

3,000,000,000

4,000,000,000

5,000,000,000

6,000,000,000

7,000,000,000

8,000,000,000

9,000,000,000

10,000,000,000

12-2003

1-2004

2-2004

3-2004

4-2004

5-2004

6-2004

7-2004

8-2004

9-2004

10-2004

11-2004

12-2004

1-2005

2-2005

3-2005

4-2005

5-2005

6-2005

7-2005

8-2005

9-2005

10-2005

11-2005

12-2005

1-2006

2-2006

3-2006

4-2006

5-2006

6-2006

7-2006

8-2006

9-2006

10-2006

11-2006

12-2006

Client cumBroker cum

Broker market analysis

Commod Average WeightNI 17.07%CU 16.50%ZN 13.47%AL 12.56%NG 8.09%AIG 7.26%WTI 6.91%AG 5.39%XAU 3.75%PB 3.51%EN 1.04%CL 1.04%XAG 0.78%BR 0.78%IM 0.62%GSCI 0.41%PM 0.21%LV 0.21%

Morgan Stanley15

UBS14

BNP13

Calyon12

MPS Finace11

Soc Gen10

CIBC9

ML8

JPM7

ABN6

Citibank5

AIG4

Deutsche3

Goldman2

Barclays1

Characteristics of Commodities: 1

• Tenor and liquidity

15 8,873,721 211 177,474,415 4,223 Sn

11,607,919 941,346 232,158,373 18,826,925 Ag

15 15,128,930 1,229 302,578,591 24,578 Pb

36,023,621 52,053 720,472,417 1,041,060 Pd

27 40,809,965 2,887 816,199,308 57,730 Zn

145,369,995 51,118 2,907,399,902 1,022,354 Pt

27 269,928,574 1,748 5,398,571,488 34,963 Ni

60 681,994,528 10,582 13,639,890,561 211,639 Al

60 682,281,528 3,656 13,645,630,552 73,127 Cu

LME Clearing Months USD Lots USD Lots Metal

Daily Monthly

Tenor and liquidity Constraints

• Investor notes• Investor pays 100% (par) at issue date• Investor rcvs 100% at redemption date (T)• Investor owns P% of atm call at T • PV to issuer = Notional(1 – df – P.C(T))• Solve for P = (1 – df ) / C• Using df = 1 / (1 + rT) and Taylor Series => Numerator ~ rT• C(T) α vol.T^0.5 => Demoninator ~ vol.T^0.5• Participation ~ (r/vol) T^0.5• Participation grows with the square of time and inverse of vol• Backwardation of forward and vol structure => High participation!


• Rotation of Ali forwards 2006

Dec-06Dec-07

Dec-08Dec-09

Dec-10Dec-11

Jan-2006

Feb-2006

Mar-2006

Apr-2006

May-2006

Jun-2006

Jul-2006

Aug-2006

Sep-2006

Oct-2006

Nov-2006

Dec-2006

1500

1700

1900

2100

2300

2500

2700

2900

2700-29002500-27002300-25002100-23001900-21001700-19001500-1700


• Also Nickel

Dec-06Dec-07

Dec-08Dec-09

Dec-10Dec-11

Jan-2006

Feb-2006

Mar-2006

Apr-2006

May-2006

Jun-2006

Jul-2006

Aug-2006

Sep-2006

Oct-2006

Nov-2006

Dec-2006

1500

6500

11500

16500

21500

26500

31500

36500

31500-3650026500-3150021500-2650016500-2150011500-165006500-115001500-6500


• And recently Copper

Dec-06Dec-07

Dec-08Dec-09

Dec-10Dec-11

Jan-2006

Feb-2006

Mar-2006

Apr-2006

May-2006

Jun-2006

Jul-2006

Aug-2006

Sep-2006

Oct-2006

Nov-2006

Dec-2006

1500

2500

3500

4500

5500

6500

7500

8500

7500-85006500-75005500-65004500-55003500-45002500-35001500-2500


• Serial Vol for commodities eg NGF7

0.00%

5.00%

10.00%

15.00%

20.00%

25.00%

30.00%

35.00%

40.00%

45.00%29/12/2006

30/11/2006

01/11/2006

04/10/2006

06/09/2006

08/08/2006

11/07/2006

12/06/2006

12/05/2006

13/04/2006

16/03/2006

15/02/2006

18/01/2006

16/12/2005

16/11/2005

19/10/2005

21/09/2005

23/08/2005

26/07/2005

27/06/2005

27/05/2005

29/04/2005

01/04/2005

03/03/2005

02/02/2005

04/01/2005

03/12/2004

0.00

10,000.00

20,000.00

30,000.00

40,000.00

50,000.00

60,000.00

70,000.00

80,000.00

90,000.00

VolOI

Case Study 1: Forward Start optioni Commodity W(i) Commodity Reference Price P(i)

1 Brent Crude 1/4 The closing settlement price per barrel of Brent

blend crude oil on the IPE of the futures contract in

respect of the first nearby month, stated in U.S.

dollars, as made public by the IPE

2 Aluminium 1/4 The official settlement price per tonne of high grade

primary aluminium on the LME for cash delivery,

stated in U.S. dollars, as determined by the LME

3 Nickel 1/4 The official settlement price per tonne of Primary

Nickel on the LME for cash delivery, stated in U.S.

dollars, as determined by the LME

4 Zinc 1/4 The official settlement price per tonne of Special

High Grade Zinc on the LME for cash delivery,

stated in U.S. dollars, as determined by the LME

Trade Date 05 March 2007

Strike Date 05 April 2007

Issue Date 14 April 2007

Valuation Date 05 April 2012

Maturity Date 12 April 2012

On the Maturity Date, the Issuer shall pay to the Note holder in respect of each Note an amount determined as follows:

Redemption = Notional [ 100% + )1;0( −finalBasketMAX

⎥⎥⎦

⎤

⎢⎢⎣

⎡=∑

= Initiali

Finali

iiFinal P

PWBasket

)(

)(4

1)(

where

FinaliP )( = the Commodity Reference Price P(i) of the Commodity (i) on the Valuation Date

InitialiP )( = the Commodity Reference Price P(i) of the Commodity (i) on the Strike Date, being in respect of each

Commodity:

Case Study 1: Hedging Forward Start risk

KC∂∂

+=Δ

55

60

65

70

75

80

85

90

95

100

105

110

115

120

1

ABC

FC∂∂

−=Δ

5.33%E[Fwd Start ]

40%10%C

20%5%B

10%1%A

DeltaE[Call]Scenario

Forward Start Risk depends on:Forward Start Risk depends on:Length of Forward StartLength of Forward StartVolatility of UnderlyingVolatility of UnderlyingCorrelation between front and back Correlation between front and back Convexity of the DerivativeConvexity of the Derivative

Example: NG forward start starting Oct, Striking Dec

Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May2002 2003 2004 2005

PriceUSDBTU

2.7

3.3

3.6

3.9

4.2

4.5

4.8

5.1

5.4

5.7

6.3

6.6

6.9

7.2

7.5

7.8

8.1

8.4

8.7

9.3

9.6

9.9

10.2

10.5

10.8

11.1

11.4

11.7

12.3

12.6

3

6

9

12

QNGc1, Last Trade, Bar11/05/2005 6.691 6.750 6.600 6.725QNGc1, Close(Last Trade), MA 1411/05/2005 6.771

3

4

5

6

7

8

9

10

28 June 2003

22 June 2004

17 June 2005

12 June 2006

07 June 2007

01 June 2008

27 May 2009

22 May 2010

17 May 2011

11 May 2012

06 May 2013

01 May 2014

26 April 2015

20 April 2016

15 April 2017

Case Study 2: Quanto options

• Example of fx hybrid• Option Payoff = EUR_Notional * max [F/K -1,0] where F is USD asset• => Variable notional option on s• Analytic Solution by ‘quantoing’ the forward• 1. Correlation sensitivity proportional to delta of the option

• 2. Commodity delta equal to product of usual delta and correlation adjustment

TFeF ρσσ 21'=

TTFeFFCC ρσσσσ

ρρ21

21'

'Δ=

∂∂

∂∂

=∂∂

TeFF

FC

FC ρσσ 21

''

Δ=∂∂

∂∂

=∂∂

Historic Correlation: DJAIG and EUR

• Monthly observations • Historic Data sample: 1 year

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

Feb-92Aug-92Feb-93Aug-93Feb-94Aug-94Feb-95Aug-95Feb-96Aug-96Jan-97Jul-97Jan-98Jul-98Jan-99Jul-99Jan-00Jul-00Jan-01Jul-01Jan-02Jul-02D

ec-02Jun-03D

ec-03Jun-04D

ec-04Jun-05D

ec-05Jun-06D

ec-06Jun-07D

ec-07

Percentiles 250 500 7500 5.8% 6.6% 6.7%

10% 7.5% 6.9% 6.8%20.0% 14.6% 8.7% 7.3%30.0% 23.0% 15.4% 8.9%40.0% 27.9% 22.1% 15.1%50.0% 37.0% 25.8% 19.4%60.0% 38.3% 26.7% 21.3%70.0% 49.6% 37.0% 25.8%80.0% 50.8% 37.1% 25.8%90.0% 53.1% 37.3% 25.9%

100.0% 59.2% 38.2% 26.7%

Case study 3: AutocallsBarr1

Underlying Size Exp CP Exp K KO? UP? Start End Bar RebateGSENER 10,000,000 06-May-08 P 06-May-08 100 FALSE FALSE 05-May-08 06-May-08 55 0

Barr2KO? UP? Start End Bar Rebate

TRUE TRUE 05-Nov-05 06-Nov-05 90 0TRUE TRUE 05-May-06 06-May-06 90 0TRUE TRUE 05-Nov-07 06-Nov-07 90 0TRUE TRUE 05-May-07 06-May-07 90 0TRUE TRUE 05-Nov-07 06-Nov-07 90 0TRUE TRUE 05-May-08 06-May-08 90 0

Barr1Underlying Size Exp CP Exp K KO? UP? Start End Bar RebateGSENER 10,000,000 06-May-08 P 06-May-08 0 TRUE FALSE 05-Nov-05 06-Nov-05 90 6.85-

Barr1Underlying Size Exp CP Exp K KO? UP? Start End Bar RebateGSENER 10,000,000 06-May-08 P 06-May-08 0 TRUE FALSE 05-May-06 06-May-06 90 9.66-


TRUE TRUE 05-Nov-05 06-Nov-05 90 0



TRUE TRUE 05-Nov-05 06-Nov-05 90 0TRUE TRUE 05-May-06 06-May-06 90 0



TRUE TRUE 05-Nov-05 06-Nov-05 90 0TRUE TRUE 05-May-06 06-May-06 90 0TRUE TRUE 05-Nov-07 06-Nov-07 90 0



TRUE TRUE 05-Nov-05 06-Nov-05 90 0TRUE TRUE 05-May-06 06-May-06 90 0TRUE TRUE 05-Nov-07 06-Nov-07 90 0TRUE TRUE 05-May-07 06-May-07 90 0



TRUE TRUE 05-Nov-05 06-Nov-05 90 0TRUE TRUE 05-May-06 06-May-06 90 0TRUE TRUE 05-Nov-07 06-Nov-07 90 0TRUE TRUE 05-May-07 06-May-07 90 0TRUE TRUE 05-Nov-07 06-Nov-07 90 0

Redemption:

(subject to early redemption)

• 100% if Index(min) > Index(initial) * KI

• )()(

initialIndexfinalIndex

capped at 100% otherwise

KI 55%

Early Redemption: If on Observation Date(i), Index(i) > 90% * Index(initial), the note redeems at the

Early Redemption Amount(i) on the Early Redemption Date(i)

• Index(i): the fixing of the index on Observation Date(i)

• Observation Date(i): see table below

• Early Redemption Date(i): see table below

• Early Redemption Amount(i): see table below

i Observation Date Early Redemption Date Early Redemption Amount

1 07/11/05 14/11/05 103.25%

2 08/05/06 15/05/06 106.50%

3 06/11/06 13/11/06 109.75%

4 07/05/07 14/05/07 113.00%

5 06/11/07 13/11/07 116.25%

6 06/05/07 27/05/08 119.50%

Autocalls: Implied Digitals

• Bet-size = 1 + coupon – df• 5 year USD df = 0.78• Standard market size = 50m => Implied Bet ~ 10m• Digital = Notional * max [s-k,0] – Notional * max [s-

(k+dk),0]• => Notional = Bet-size / dk

-

2,000,000.00

4,000,000.00

6,000,000.00

8,000,000.00

10,000,000.00

12,000,000.00

80 85 90 95 100 105 110 115

10,000,000 Metal Price 2% Lots per tonVolume Volume:DaCu 5,500 110 25 3,636 1.0 Al 2,600 52 25 7,692 0.7 Ni 33,000 660 6 2,525 1.4 Pt 1,100 22 1 454,545 8.9 Zn 3,880 78 25 5,155 1.8 Pd 330 7 1 1,515,152 29.1 Pb 1,600 32 25 12,500 10.2 Ag 12 0 1 41,666,667 44.3 Sn 11,000 220 5 9,091 43.1

Autocalls: Intra-asset correlation riskFwd1 Fwd2 Intrinsic KI? * Instrinsic

105 0% 0 0%

110 100

95 5% 0 0%100

105 0% 1 0%

90 100

95 5% 1 5%

2.5%+100%1.25%0%0%-100%E[KI Put]Correlation

Case Study 4: Dispersion

Buyer receives: Not * ⎟⎟

⎠

⎞⎜⎜⎝

⎛ −∑= )(mod

)(mod)(mod%,0*1

1 initialityCominitialityComfinalityCom

Maxn i

iin

i

Where: For i = 1 to n, n being the number of commodities in the basket Commodityi (initial): The Official Closing Price of Commodity i as of the Strike Date. Commodityi (final): The Official Closing Price of Commodity i as of the Expiry Date. Not = Basket Notional Amount NB: Currency of payoff – USD.

Seller receives: Not * ⎟⎟⎠

⎞⎜⎜⎝

⎛ −∑=

n

i i

ii

initialityCominitialityComfinalityCom

nMax

1 )(mod)(mod)(mod1%,0

Where: For i = 1 to n, n being the number of commodities in the basket Commodityi (initial): The Official Closing Price of Commodity i as of the Strike Date. Commodityi (final): The Official Closing Price of Commodity i as of the Expiry Date. Not = Basket Notional Amount NB: Currency of payoff – USD.

Case 4: Dispersion Payoff

Asset1 Asset2 Buyer Seller Dispersion120 15% 15% 0%

110 100

80 5% 0% 5%100

120 10% 5% 5%

90 100

80 0% 0% 0%

0%+100%2.5%0%5%-100%E[Dispersion]Correlation

Aviation and Exotics rule:

Take-offs are optional… …Landings are mandatory

Groves

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