Rags or Riches: Short Options Trading Program

FIRST EUBANK CONFERENCE: MODELING REAL WORLD MARKETS

Rice UniversityMarch 24, 2009

George R. Brown School of Engineering STATISTICS

2

DJIA, 1925 - 1955

DJI

A In

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x

1925 1930 1935 1940 1945 1950 1955

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0Objective

33

Why We Are Here

Conference Results TRU

Performance

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0 10 20 30 40 50

Years Since Purchase

Valu

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f In

itia

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oll

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Tim

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T-Bill

S&P 500

MaxMedian

#REF!

44

Global WarningBrazil BVSP

Days, 1/2000 - 12/2008

Ind

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0 500 1000 1500 2000

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German DAX

Days, 1/2000 - 12/2008

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80

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Japan Nikkei 225

Days, 1/2000 - 12/2008

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0 500 1000 1500 2000

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China Shanghai SSEC

Days, 1/2000 - 12/2008

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0 500 1000 1500 2000

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55

Outline

• Data

• Benchmarks

• Overview of Option Trading Program

• Parametric results

• Resampling results

• BSOPM results

• Conclusion and Future Work

66

Data

• Data Acquisition and Cleaning– E100 Portfolio – 1/2/90 thru 12/31/2007 (4538 x 94)

• VIX available• CRSP available• Options widely traded

– Used HQuote and CRSP– Non-split adjusted for options– Options trading data– Legacy Portfolio (4538 x 12)

• Realism (instead of cash)• Covered Call Program

– Challenges

7

Legacy Portfolio

7

Covered Call Portfolio - Legacy Portfolio

Name Symbol Shares BasisAM HOME PROD AHP 1000 10,623.13CITIGROUP C 2000 25,419.00GEN ELEC GE 3600 18,322.50INTEL INTC 1400 37,362.50J&J JNJ 400 5,052.50JP Morgan & Chase JPM 1200 26,108.75COCA COLA KO 4000 24,332.75PHIL MORR MO 4200 38,936.13MERCK MRK 2400 28,148.75PEPSICO PEP 1000 16,760.00PFIZER PFE 3600 21,996.00EXXON XOM 37000 396,593.75

649,655.75

88

Data AcquisitionGD

Days, 1/1990 - 12/2008

Pri

ce

0 1000 2000 3000 4000

20

40

60

80

10

0MMM

Days, 1/1990 - 12/2008

Pri

ce

0 1000 2000 3000 4000

60

80

10

01

20

14

0

SLE

Days, 1/1990 - 12/2008

Pri

ce

0 1000 2000 3000 4000

20

30

40

50

60

USB

Days, 1/1990 - 12/2008

Pri

ce

0 1000 2000 3000 4000

20

40

60

80

10

0

99

Benchmark Returns

• Always need these to keep in context (and for performance fees!)

Benchmark ReturnsAfter-tax

1/2/1990 12/31/2007 Return CAGR CAGRSPX 353.4 1468.36 4.155 0.082 0.075NYSE/AMEX - MW 10,000 43,332 4.333 0.085 0.078Legacy 652,175 4,679,544 7.175 0.116 0.107NYSE/AMEX - EW 10,000 51,900 5.190 0.096 0.088SPX + Div 10,000 60,627 6.063 0.105 0.097NYSE/AMEX - MW + Div 10,000 65,554 6.555 0.110 0.102NYSE/AMEX - EW + Div 10,000 84,844 8.484 0.126 0.117All Stocks (4,600) + Div 10,000 132,974 13.297 0.155 0.145BRKA 8,200 141,600 17.268 0.171 0.162

1010

Options Basics

• Buy calls if the market is going to go up• Buy puts if the market is going to go down• Sell options if you think the market is not going

to close outside the strike.

1 2

( , , , , )

( ) ( )rt

V V S X T r

C S d Xe d

Why Sell Options

• Hedging (“Fun” way to manage a position)

• Income Production (“Speculation”)

What It Looks Like

Option Trades for Citigroup Stock

Adj. ExitDate Trade # Open Cost/Sh Exit Price Close

07/24/00 CHO Ag 75 call (C) -10 714.92 0.715 08/18/00 0.250 285.2611/03/00 CKK Nv 55 call (C) -10 1214.91 1.215 11/18/00 Expired 011/03/00 CKL Nv 60 call (C) 10 222.5 0.223 11/18/00 Expired 002/26/01 COI Mr 45 put (C) -5 294.98 0.590 03/15/01 0.450 255.503/15/01 CPV Ap 42.5 put (C) -5 619.97 1.240 03/20/01 1.250 655.3803/27/01 CDJ Ap 50 call (C) -20 899.97 0.450 04/18/01 1.250 2535.3509/28/01 CJI Oc 45 call (C) -20 349.98 0.175 10/19/01 0.400 835.3510/01/01 CVV Oc 42.5 put (C) 10 1735.35 1.700 10/12/01 0.50 499.9802/27/02 CCW Mr 47.5 call (C) -20 229.64 0.115 03/15/02 1.950 3970.3509/26/02 CKG Nv 35 call (C) -20 929.61 0.465 11/15/02 1.750 3570.3511/15/02 CLU Dc 37.5 call (C) -20 2529.57 1.265 12/20/02 0.600 1270.3501/17/03 CBU Fb 37.5 call (C) -10 1164.79 1.165 01/29/03 0.600 670.3501/23/03 CLTOG Mr 35 put (C) 10 1185.18 1.185 01/29/03 1.35 1279.603/21/03 CDU Ap 37.5 call (C) -10 979.61 0.980 04/16/03 1.900 1970.35

1313

Option Program - BM• All positions established/closed monthly• Don’t try to guess market (Puts/Calls)• Take no assignments!• Buying power safety factor

– Has to be margin account

• Annual after-tax, STCG• Monthly proprietor draw (non-employee)• Balance remains to compound

– Could be invested in stock; Market risk if done so.

– Leave in for simulation purposes

14

Program Assumptions

• Tradeclock, centered at EOEXP– EOEXP / FDTM / EOM / EOY / BOY

• Establish positions in 1st 5 trading days

• Sell 1-Month, 1-OTM, 2-OTM

• Throw out trade if premium less than $100

• Throw out trade if a split is scheduled within the trading window

• The program does not handle blowouts

1515

Trading Program

• Parametric Trading Program– Opening premium distribution– Closing premium distribution

1,272 564 349 403 807 1,935 441634 469 234 2,646 1,666 2,009 803902 392 1,435 2,035 2,182 391 507264 280 290 291 1,111 679 290

6,196 744 1,376 401 261 420 5451,219 314 1,019 725 416 345 517

425 306 500 1,059 271 670 1,397529 654 589 269 5,824 757 3,018456 301 420 720 362 207 1,777436 695 586 656 244 619 431572 761 614 364 416 374 424307 509 404 898 1,076 443 431473 401 647 353 240 409 1960

1,998 3,232 828 262 888 326 1606695 1,199 839 1,583 3,391 237 469

1616

Parametric Program

• Parametric 1 – Fixed number of positions each month

• 1 position/day = 5 positions/month• 2 position/day = 10 positions/month

– Draw and tax rates 10%

• Parametric 2 – Number of portions determined by buying power– Upped tax rate to 25% at this stage; draw 10%

• Parametric 3– Actual trading position parameters– large trading losses

1717

Parametric 1

• Fixed number of positions; tax=10%, draw 10%. Open: lognormal; Close: Bernoulli/lognormal

• Cash only, A0=100,000

• Cash + Legacy Portfolio

• Cash + Legacy Portfolio, tax changed to 25% (kept the draw) and increased number of positions per month to 10 instead of 5.

1818

Parametric 1• Cash only, A0=100,000

STCG Tax Cash12/31/1990 14,399 3,600 8,21812/31/1991 31,424 7,856 19,97212/31/1992 30,370 7,592 18,71912/31/1993 50,291 12,573 32,60312/30/1994 62,261 15,565 40,32412/29/1995 46,272 11,568 29,55612/31/1996 25,412 6,353 16,00012/31/1997 42,563 10,641 27,38112/31/1998 44,408 11,102 28,85812/31/1999 52,796 13,199 34,31812/29/2000 33,641 8,410 21,75212/31/2001 47,443 11,861 30,83812/31/2002 38,079 9,520 23,37512/31/2003 29,227 7,307 17,19712/31/2004 57,841 14,460 37,59712/30/2005 37,781 9,445 24,55812/29/2006 46,873 11,718 30,21812/31/2007 39,993 9,998 25,996

1919

Parametric 1

• Cash + Legacy Portfolio

Program Gain (18 yrs)

x1

Fre

quen

cy

250000 350000 450000

020

4060

8010

0

250000 350000 450000 550000

0.0

0.2

0.4

0.6

0.8

1.0

Gain Probability

x

Pro

babi

lity

Account Value (18 yrs)

x2

Fre

quen

cy

5000000 5100000 5200000

020

4060

8010

012

0

4950000 5050000 5150000

0.0

0.2

0.4

0.6

0.8

1.0

Account Value Probability

x

Pro

babi

lity

2020

Parametric 1 - FixedParametric Case, Annual Gains for Fixed Option Level

Years

GA

R.s

im

5 10 15

0.0

10

.02

0.0

30

.04

0.0

50

.06

2121

Parametric 1 - Fixed

• Cash + Legacy Portfolio, tax changed to 25%; increased positions to 10 per month

• About the same graphs as with the 10% tax case.

• Same problem with decreasing returns.

• Nonetheless, $350,000 - $760,000 more than idle assets.

2222

Parametric 2

• Dynamic number of positions• Determined by buying power

• Positions consume buying power (a 10-lot $100 strike consumes $40,000 in BP)

• Open: lognormal; Close: Bernoulli/lognormal• Tax 25%, draw 10%

margin%

C P

margin.option

margin

%

%

ptvalue k strike

2323

Parametric 2

0 50 100 150 200

02

00

04

00

06

00

0

Number of Postitions each Month

Months

Nu

mb

er

of P

osi

tion

s

0 50 100 150 200

05

00

15

00

25

00

STCG Realized Each Month

Months

$1

00

0

2424

Parametric 2Program Gain (18 yrs)

$M

Fre

quen

cy

115 125 135 145

040

8012

0

110 130 150

0.0

0.4

0.8

Gain Probability

$M

Pro

babi

lity

Account Value (18 yrs)

$M

Fre

quen

cy

80 90 100

020

4060

80

75 85 95

0.0

0.4

0.8

Account Value Probability

$M

Pro

babi

lity

2525

Parametric 2

0.20 0.25 0.30 0.35 0.40 0.45

01

00

03

00

05

00

0Annual Returns (Percent)

Precent Gain

Annual Return Probability

%

Pro

ba

bili

ty

0.20 0.25 0.30 0.35 0.40 0.45

0.0

0.2

0.4

0.6

0.8

1.0

2626

Alas, Parametric 3

• A little too good to be true

• Time to look at real data

• Parametric 3– Dynamic number of positions– Tax 25%, draw 10%– Actual trading position parameters

2727

Premium DistributionOPEN

Opening Premium

Fre

qu

en

cy

0 2000 4000 6000 8000 10000

02

00

50

0

CLOSE

Closing Premium

Fre

qu

en

cy

0 2000 4000 6000 8000 10000 12000

02

00

40

0

Min. 1st Qu. Median 10.0 312.5 800.0

Mean 3rd Qu. Max. 1555.0 1782.0 24030.0

Min. 1st Qu. Median -10.38 317.80 467.80

Mean 3rd Qu. Max. 636.80 729.60 23770.00

2828

Option Sales DataNaked Options

Total Expired Haircut Pain Disaster Castastrophy12/31/1999 12 0.417 0.500 0.083 0.000 0.00012/31/2000 469 0.729 0.186 0.030 0.038 0.01712/31/2001 1956 0.717 0.212 0.040 0.027 0.00412/31/2002 1175 0.777 0.117 0.060 0.042 0.00512/31/2003 259 0.622 0.301 0.042 0.035 0.00012/31/2004 384 0.615 0.240 0.081 0.060 0.005

4255 0.719 0.192 0.048 0.036 0.005

• Used to Match ecdf's for opening and closing positions

• Updated lognormals and Pr(expire)

2929

Parametric 3

STCG Tax Cash12/31/1990 68,882 17,220 40,30612/31/1991 61,102 15,276 35,74412/31/1992 37,746 9,436 16,50512/31/1993 62,590 15,648 24,91412/30/1994 141,484 35,371 81,50712/29/1995 171,202 42,801 110,63412/31/1996 (98,568) (24,642) (84,703)12/31/1997 244,718 61,180 155,51212/31/1998 290,736 72,684 187,08412/31/1999 277,429 69,357 179,06312/29/2000 320,377 80,094 193,37912/31/2001 (33,243) (8,311) (57,970)12/31/2002 439,279 109,820 269,94512/31/2003 448,791 112,198 287,42212/31/2004 398,015 99,504 254,21012/30/2005 507,667 126,917 317,42012/29/2006 655,213 163,803 420,94612/31/2007 258,595 64,649 141,205

3030

Parametric 3Program Gain (18 yrs)

$M

Fre

quen

cy

0 1 2 3 4 5 6 7

050

100

150

200

250

0 2 4 6

0.0

0.2

0.4

0.6

0.8

1.0

Gain Probability

$M

Pro

babi

lity

Account Value (18 yrs)

$M

Fre

quen

cy

4 5 6 7 8 9

010

020

030

040

0

4 5 6 7 8 9

0.0

0.2

0.4

0.6

0.8

1.0

Account Value Probability

$M

Pro

babi

lity

3131

But…

-2.5 -2.0 -1.5 -1.0 -0.5 0.0

02

00

60

01

00

01

40

0

Annual Returns (Percent)

Precent Gain

Annual Return Probability

%

Pro

ba

bili

ty

-2.5 -2.0 -1.5 -1.0 -0.5 0.0

0.0

0.2

0.4

0.6

0.8

1.0

3232

A Closer LookAnnual Returns

Trial Year

Acc

ou

nt

Re

turn

0 5000 10000 15000

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

3333

Extreme ValuesUnfortunate Large Numbers

Position Closeout Amount, $100k

Fre

qu

en

cy

0 5 10 15 20 25 30 35

05

01

00

15

02

00

25

03

00

34

Resampling Approach

• Resampling using Trading Data

• Sample with replacement– Opening positions– Closing positions– No probability of expiration

• Summary(GAR.sim, M=6000) Min. 1st Qu. Median Mean 3rd Qu. Max.

-0.0166 0.1526 0.1822 0.1829 0.2123 0.3795

3535

Resampling Results

0 50 100 150 200

20

06

00

10

00

14

00

Number of Postitions each Month

Months

Nu

mb

er

of P

osi

tion

s

0 50 100 150 200

01

00

20

03

00

STCG Realized Each Month

Months

$1

00

0

3636

Resampling ResultsProgram Gain (18 yrs)

$M

Fre

quen

cy

18 20 22 24 26 28

020

060

0

16 20 24 28

0.0

0.4

0.8

Gain Probability

$M

Pro

babi

lity

Account Value (18 yrs)

$M

Fre

quen

cy

16 18 20 22

020

040

0

16 18 20 22 24

0.0

0.4

0.8

Account Value Probability

$M

Pro

babi

lity

3737

Resampling Results

0.0 0.1 0.2 0.3

05

00

10

00

15

00

20

00

Annual Returns (Percent)

Precent Gain

Annual Return Probability

%

Pro

ba

bili

ty

0.0 0.1 0.2 0.3

0.0

0.2

0.4

0.6

0.8

1.0

38

Benchmarks Revisited

• Does NOT include Legacy return

Benchmark ReturnsAfter-tax

1/2/1990 12/31/2007 Return CAGR CAGRSPX 353.4 1468.36 4.155 0.082 0.075NYSE/AMEX - MW 10,000 43,332 4.333 0.085 0.078Legacy 652175 4679544 7.175 0.116 0.107NYSE/AMEX - EW 10,000 51,900 5.190 0.096 0.088SPX + Div 10,000 60,627 6.063 0.105 0.097NYSE/AMEX - MW + Div 10,000 65,554 6.555 0.110 0.102NYSE/AMEX - EW + Div 10,000 84,844 8.484 0.126 0.117All Stocks (4,600) + Div 10,000 132,974 13.297 0.155 0.145BRKA 8,200 141,600 17.268 0.171 0.162

Resampling Option Program 0.182 Min. 1st Qu. Median Mean 3rd Qu. Max. -0.01659 0.1526 0.1822 0.1829 0.2123 0.3795

39

BSOPM Program

• A necessary fiction

• Historical parameter estimation

• Implied volatility approximation

• How to handle splits (only 4/94 didn’t split)

• Results to be shown– Covered calls only– Uncovered fixed number of options– Covered calls and dynamic uncovered options

A Necessary Fiction

40

41

Parameter Estimation

Number Observations Used in Estimate, N_max = 30732

Est

ima

te (

An

nu

aliz

ed

)

0 200 400 600 800 1000 1200

0.0

0.0

50

.10

0.1

50

.20

mu_hat

sigma_hat

GBM Parameter Estimates for DJX by N

GBM Estimates

Number Observations Used in Estimate, N_max = 30000

Est

ima

te (

An

nu

aliz

ed

)

0 200 400 600 800 1000 1200

0.0

0.0

50

.10

0.1

5

mu_hat

sigma_hat

GBM Parameter Estimates for SGBM by N

43

IV ApproximationGamma

Days

Ga

mm

a

1990 1995 2000 2005

-4-3

-2-1

01

Kappa Factor Est.

Days

Fa

cto

r

1990 1995 2000 2005

0.6

0.8

1.0

1.2

1.4

(1 )IV IVj j SPX j

44

Covered Calls Only

• Same trading methodology

• DO NOT LOSE STOCK!

• Sell 1- or 2- strike OTM

• Only sell 1-month until expiration

• Cover on last trading day if ITM.

• Pretend never get called away – may really happen, even if OTM.– Real-life mitigation techniques

4545

Covered Calls OnlyXOM, 2005-2007

Days, 1/1/2005 - 12/31/2007

Le

ga

cy[3

78

4:4

53

8,

"XO

M"]

0 200 400 600

50

60

70

80

90

1,850,000

3,515,000

4646

Covered Calls OnlyBSOPM Covered Call Program Only BSOPM Naked Options Only

1-Strike OTM 2-Strike OTMSTCG Cash STCG Cash

12/31/1990 29,692 17,949 384 25012/31/1991 4,093 396 307 19912/31/1992 (4,043) (5,497) NA NA12/31/1993 (20,083) (16,409) NA NA12/30/1994 19,937 12,633 NA NA12/29/1995 (52,518) (41,222) NA NA12/31/1996 5,022 1,663 228 14812/31/1997 2,111 (9,092) 21,701 13,37212/31/1998 33,331 9,267 40,542 25,48012/31/1999 264,555 165,010 102,455 66,59612/29/2000 237,223 149,341 71,185 45,22212/31/2001 540,868 351,564 134,651 87,52312/31/2002 86,885 32,137 60,126 38,78812/31/2003 108,069 64,154 31,926 20,75212/31/2004 (67,305) (55,998) 2,569 1,67012/30/2005 (436,314) (338,626) (29,972) (22,892)12/29/2006 (137,778) (116,953) 7,945 5,01912/31/2007 (413,701) (333,420) (39,375) (33,738)

200,044 (113,103) 404,672 248,389

47

Uncovered options

• Compare selling 1-strike and 2-strike OTM • Compare fixed amount of symbols per day

for 5 days to establish– 1 symbol per day (up to 10 positions/month)– 10 symbols per day (up to 100 pos/mo.)– might have less

• Dynamic establish (based on buying power)– run out of stocks– results in multiple positions– Still realistic

4848

Uncovered, 1 SymbolBSOPM Naked Options Only BSOPM Naked Options Only

1-Strike OTM 2-Strike OTMSTCG Cash STCG Cash

12/31/1990 37,497 23,852 8,952 5,44512/31/1991 (11,575) (9,555) 2,092 1,21112/31/1992 (16,697) (13,008) (575) (723)12/31/1993 (18,737) (15,591) 2,277 1,48012/30/1994 8,095 4,494 310 (2)12/29/1995 (8,683) (7,899) 6,248 3,97912/31/1996 15,159 8,535 236 (657)12/31/1997 1,645 (4,401) 29,834 18,98412/31/1998 6,356 (1,697) 48,834 30,92412/31/1999 7,055 1,440 27,583 16,42112/29/2000 (4,573) (7,892) (11,984) (11,856)12/31/2001 47,125 28,900 (7,423) (6,789)12/31/2002 10,324 3,933 15,970 9,57512/31/2003 38,967 24,784 9,596 6,02712/31/2004 3,389 886 97 6312/30/2005 (7,094) (6,521) 734 47712/29/2006 (3,673) (3,858) (14,679) (11,288)12/31/2007 264 (3,431) 5,564 3,386

104,844 22,971 123,666 66,657

4949

Uncovered, 10 SymbolBSOPM Naked Options Only

1-Strike OTM 2-Strike OTMSTCG Cash STCG Cash

12/31/1990 259,964 162,015 136,435 88,63912/31/1991 (46,535) (42,278) (14,502) (15,775)12/31/1992 (172,061) (132,695) (53,215) (41,146)12/31/1993 (151,493) (115,518) (48,672) (37,132)12/30/1994 (113,855) (89,417) 11,036 6,05612/29/1995 (206,181) (157,069) 3,194 31512/31/1996 (98,756) (80,926) (39,185) (31,984)12/31/1997 409,785 256,987 135,363 83,70512/31/1998 331,451 206,992 173,647 106,70012/31/1999 391,382 237,165 193,012 118,52312/29/2000 (70,135) (68,372) (58,683) (50,920)12/31/2001 199,548 108,302 89,969 53,36512/31/2002 48,423 13,372 38,676 19,45512/31/2003 257,576 165,661 98,377 63,55012/31/2004 33,031 16,154 14,531 9,29212/30/2005 (49,759) (43,354) 8,615 4,99912/29/2006 (86,718) (69,787) (474) (1,857)12/31/2007 112,180 60,468 (26,629) (25,096)

1,047,847 427,700 661,495 350,689

50

Uncovered, Fixed10/month, 1 OTM

$M

Fre

quen

cy

-0.1 0.1 0.2 0.3

05

1015

2025

10/month, 2 OTM

$M

Fre

quen

cy

-0.05 0.05 0.15 0.25

010

2030

40

100/month, 1 OTM

$M

Fre

quen

cy

0.6 1.0 1.4

05

1015

2025

100/month, 2 OTM

$M

Fre

quen

cy

0.6 0.8 1.0 1.2 1.4

05

1015

2025

30

51

Uncovered, DynamicGain, 1-Strike

$M

Fre

quen

cy

5 6 7 8 9 10 11

010

2030

4050

6070

Gain, 2-Strike

$M

Fre

quen

cy

3.5 4.5 5.5 6.5

010

2030

4050

60

Account, 1-Strike

$M

Fre

quen

cy

7 8 9 10 11

020

4060

8010

0

Account, 2-Strike

$M

Fre

quen

cy

7.0 7.5 8.0 8.5 9.0

020

4060

80

52

Annual ReturnsReturns, 1-Strike

Percent Return

Fre

quen

cy

-0.4 -0.2 0.0 0.2 0.4

020

040

060

080

010

00

Returns, 2-Strike

Percent Gain

Fre

quen

cy

-0.1 0.0 0.1 0.2 0.3 0.4

020

040

060

080

010

00

-0.6 -0.2 0.0 0.2 0.4 0.6

0.0

0.2

0.4

0.6

0.8

1.0

Probability

%

Pro

babi

lity

-0.2 0.0 0.1 0.2 0.3 0.4

0.0

0.2

0.4

0.6

0.8

1.0

Probability

%

Pro

babi

lity

53

Return Comparison

-3.0 -2.0 -1.0 0.0

02

46

8

Returns, Parametric 3

Annual Return

Den

sity

0.0 0.1 0.2 0.3 0.4

02

46

8

Resampling

Annual Return

Den

sity

-0.6 -0.2 0.2 0.4 0.6

0.0

0.5

1.0

1.5

2.0

2.5

BSOPM 1-Strike

Annual Return

Den

sity

-0.2 0.0 0.1 0.2 0.3 0.4

02

46

BSOPM 2-Strike

Annual Return

Den

sity

54

Toward Conclusion

• Bimodality of annual returns caused by winning and losing years

• Accumulated cash position key to program performance

55

Cash PositionTypical Cash, 1-Strike OTM

Time

$M

1990 1995 2000 2005

-10

12

34

5

Typical Cash, 2-Strike OTM

Time

$M

1990 1995 2000 2005

-10

12

34

5

56

Cash, Big DrawCash, 65% Draw, 1-Strike

Time

$M

1990 1995 2000 2005

-3-2

-10

1

Cash, 65% Draw, 2-Strike

Time

$M

1990 1995 2000 2005

-3-2

-10

1

57

Optimal Draw ICash, 10% Draw, 1-Strike

Time

$M

1990 1995 2000 2005

-20

24

6

Cash, 35% Draw, 1-Strike

Time

$M

1990 1995 2000 2005

-20

24

6

Cash, 45% Draw, 1-Strike

Time

$M

1990 1995 2000 2005

-3-2

-10

1

Cash, 65% Draw, 1-Strike

Time

$M

1990 1995 2000 2005

-3-2

-10

1

58

Optimal Draw IICash, 10% Draw, 2-Strike

Time

$M

1990 1995 2000 2005

-20

24

6

Cash, 35% Draw, 2-Strike

Time

$M

1990 1995 2000 2005

-20

24

6

Cash, 45% Draw, 2-Strike

Time

$M

1990 1995 2000 2005

-3-2

-10

1

Cash, 65% Draw, 2-Strike

Time

$M

1990 1995 2000 2005

-3-2

-10

1

59

Conclusions

• Idle assets have untapped buying power

• It is possible to sell time premium

• Hard to code trader’s skill/performance

• Resampling results show promising return

• BSOPM with approximations gives mixed results.– ITM vectors still not compensated for by

market prices, however

• Do not withdraw all the money!

6060

Future Work

• More Data– Spreads– Assignments

• Dynamic universe

• Historical option prices– Or better IV approximation– Not that far off

• Laddering of large positions

• Simulation of future results– many challenges

61

A Special Thanks To:

• Eubank Benefactors

• Prof. J.R. Thompson

• Prof. E.E. Williams

• Prof. K.B. Ensor

• TRU – Dept. of Statistics

• Stock Exchanges Options Trading Antitrust Litigation– c/o Berdon Claims Adminstration, LLC