The Importance of Relationships

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Mar 20, 2003 ... The Importance of Relationships. Sheldon Natenberg. Chicago Trading Co. 440 S. LaSalle St. Chicago, IL 60605. (312) 863-8004 ...

The Importance of Relationships Sheldon Natenberg Chicago Trading Co. 440 S. LaSalle St. Chicago, IL 60605 (312) 863-8004

All option trading decisions depend on relationships. How do we define or model the relationship? How reliable is the relationship? How great is the mispricing in the marketplace?

Arbitrage Relationships Put / Call / Parity C - P = (F - X) / (1+r*t) C - P = S - [X / (1+r*t)] - D Well defined Very reliable Done in big size

Logical Relationships SPX = 800.00 June 800 straddle = 90 June 850 straddle = 85 Based on assumptions about market dynamics Not always reliable Done in limited size

Relationships Based On Volatility Term Structure Skew and Kurtosis Inter-Market Correlations A Combination of the Above

DJX Implied Volatilities vs. Time to Expiration - 12 March 2003 35%

34%

33%

32%

31%

30%

29%

28%

27%

26%

25% 0

2

4

6

8

10

12 months to expiration

14

16

18

20

22

24

DJX Implied and Forward Volatilities - 12 March 2003 35%

34%

33%

32%

31%

30%

29%

28%

27%

26%

25% 0

2

4

6

8

10

12 months to expiration

14

16

18

20

22

24

SPX Daily Price Changes: January 1990 - December 2002 250

225

200

number of occurrences

175

150

number of days: 3281 biggest up move: +5.73% (24 July 2002) biggest down move: -6.87% (27 October 1997) mean: +.0345% standard deviation: 1.0561% volatility: 16.78% skewness: +.0022 kurtosis: +3.8361

125

100

75

50

25

0 -7%

-6%

-5%

-4%

-3%

-2%

-1%

0%

daily price change (nearest 1/8 percent)

1%

2%

3%

4%

5%

SPX March 03 Implied Volatilities - 28 December 2002 (SPX = 875.40) 44 42 40 38 36 34 32 30 28 26 24 22 20 550

600

650

700

750

800

850

900

950

1000

1050

1100

1150

SPX Implied Volatilities - 28 December 2002 (SPX = 875.40) 50

Jan03 (872.74 / 27.39) 45

Feb03 (872.3 / 27.5) Mar03 (871.33 / 28.02) Jun03 (870.47 / 27.13) Sep03 (869.73 / 26.68) Dec03 (869 / 26.39)

40

Jun04 (870.08 / 25.99) Dec04 (877.1 / 25.88)

35

30

25

20 500

600

700

800

900

1000

1100

1200

1300

1400

SPX Implied Volatilities - 28 December 2002 (SPX = 875.40) 50

Jan03 (872.74 / 27.39) Feb03 (872.3 / 27.5)

45

Mar03 (871.33 / 28.02) Jun03 (870.47 / 27.13) Sep03 (869.73 / 26.68) Dec03 (869 / 26.39)

40

Jun04 (870.08 / 25.99) Dec04 (877.1 / 25.88)

35

30

25

20 -1.50

-1.25

-1.00

-0.75

-0.50

-0.25 ln(X/F) / sqrt(t)

0.00

0.25

0.50

0.75

1.00

1400

2800

SPX

2600

NDX

1300

2400

2200

1200

2000 1100 1800

SPX

NDX 1600 1000 1400

900

1200

1000 800 800

700 Jan-01

Apr-01

Jul-01

Oct-01

Jan-02

Apr-02

Jul-02

Oct-02

600 Jan-03

SPX / NDX 50-day Historical Volatilities: January 2001 to December 2002 90%

80%

SPX NDX

70%

60%

50%

40%

30%

20%

10%

0% Jan-01

Apr-01

Jul-01

Oct-01

Jan-02

Apr-02

Jul-02

Oct-02

Jan-03

SPX vs. NDX Correlation: 2001 - 2002 20%

y = 1.6879*x - .0001 15%

r = .818 NDX - percent daily price change

10%

r2 = .669 5%

0%

-5%

-10%

-15% -6%

-5%

-4%

-3%

-2%

-1%

0%

1%

SPX - percent daily price change

2%

3%

4%

5%

6%

MNX / SPX Volatility Ratios

1.45

1.40

1.35

1.30

1.25

1.20

1.15

1.10

1.05 0

2

4

6

8

10

12 months to expiration

14

16

18

20

22

24

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