Stock Options 101

Lindsay Yoshitomi

Leslie White

Jennifer Jones

Jeff Guba

Stock Option?

-Contracts that give you the option to buy or sell shares of a particular stock for a set price. (You are not obligated to do it!)

-Call Option: option allowing holder to buy stock.

-Put Option: option allowing holder to sell stock.

What is a good value/price for your stock option on its start date: March 21, 2003?

Our Initial Estimate: $58.67

Strike Price- Pre-specified price at which the holder of a call can buy the stock or holder of put can sell stock.

Risk Free Rate- Current T-Bill rate return, on safe investment.

Length of option- the time in which one must wait to exercise a European Option in which an investor can purchase shares of particular stock.

# of years to download- the necessary information needed to research the price of a particular stock for a certain time period.

Volatility- the amount of change in a specified stock, increase or decrease.

Stock : Johnson and Johnson Ticker Symbol:

JNJ

Strike Price:

$40

Length of Option:

17 weeks

Risk Free Rate:

1.20%

# of Years to Download:

12 years

%023077.0%10000023077.052

012.0

52

rrrf

-Since we are dealing with the option in terms of weeks, we need to convert our annual risk-free rate into a weekly rate.

Step 1:

weekly closing prices Ratios BeforeDayoficegClo

icegClosToday

___Pr_sin

Pr_sin_'

-This continues down the column, but the last value is zero because there is nothing to divide it by.

stockrif

stockrif

_1_

_1_

Step 2:

To compute the Max, Min, Average & Range of our ratios, we used the built-in Excel functions MAX, MIN, and AVERAGE for the first three calculations

(=MAX, =MIN, =AVERAGE with the cell references). To find the Range, simply subtract the minimum from the maximum.

Therefore:MAX = 1.185596907MIN = 0.828594313AVERAGE = 1.003545923RANGE = 0.357002594

Johnson & Johnson Stock Data

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.84644 0.88214 0.91784 0.95355 0.98925 1.02495 1.06065 1.09635 1.13205 1.16775 1.20345

Ratios for Adjusted Clos ing Price

Rel

ativ

e F

req

uen

cy

bins Frequency Percentage Labels

0.852394 1 0.00160256 0.840494

0.876195 0 0 0.852394

0.899995 1 0.00160256 0.864295

0.923795 4 0.00641026 0.876195

0.947595 21 0.01365385 0.888095

0.971395 62 0.02935897 0.899995

0.995196 166 0.12602564 0.911895

1.018996 184 0.42487179 0.923795

1.042796 118 0.33910256 0.935695

1.066596 46 0.07371795 0.947595

1.090396 11 0.01762821 0.959495

1.114196 6 0.00961538 0.971395

1.137997 3 0.00480769 0.983295

1.161797 0 0 0.995196

1.185597 1 0.00160256 1.007096

More 0

624

-Let be a continuous random variable representing the normalized ratios.

normR

)( rfmnorm RRRR

a.) R= the ratio

mRb.) = average of the ratios

c.) rfR =risk-free weekly ratio

)000230797.1003545923.1()1_( weekRRnorm

)000230797.1003545923.1()17_( weekRRnorm

000230797.1

)00023077.0(

ee

eR

rfr

rfrrf

Bar Graph of p.d.f Normalized Ratios

0 2 4 6 8 10 12 14

3.180865572

3.198715702

3.216565832

3.234415961

3.252266091

3.270116221

3.28796635

3.30581648

3.32366661

3.341516739

Line Graph of p.d.f. Normalized Ratios

0

2

4

6

8

10

12

14

3.180866 3.198716 3.216566 3.234416 3.252266 3.270116 3.287966 3.305816 3.323667 3.341517

-The difference between a histogram and the bar and line graph is that the area under the graph is the probability.

To create a simulation the following functions were used to determine the future value of our stock option:

IF

VLOOKUP

RANDBETWEEN

future value

=IF( Week 17 closing price>40(strike price),week 17-40,0)

= I8 * VLOOKUP(RANDBETWEEN(1,625),$A$2:$D$626,4,)

Start Price

                   

Stock Data              

Option Data

run

start (3/21)

week 1

week 2

week 3

week 4

week 5

week 6

week 7

week 8

week 9

week 10

week 11

week 12

week 13

week 14

week 15

week 16

week 17 FV PV

1$58.67

$55.62

$49.87

$50.19

$49.88

$49.80

$49.99

$55.42

$54.13

$54.89

$55.82

$56.27

$60.54

$59.62

$60.47

$61.54

$63.29

$64.19

$24.19

$24.09

2$58.67

$59.31

$63.68

$63.57

$64.56

$65.65

$68.02

$71.42

$69.20

$68.30

$67.19

$66.55

$69.17

$68.39

$71.99

$71.75

$67.92

$69.11

$29.11

$28.99

3$58.67

$56.09

$56.41

$55.26

$62.54

$66.04

$68.45

$64.89

$64.19

$65.85

$64.97

$66.68

$68.49

$74.67

$77.97

$86.44

$90.25

$84.55

$44.55

$44.38

4$58.67

$62.61

$64.23

$63.92

$63.63

$66.17

$65.11

$63.48

$71.85

$73.32

$73.69

$73.12

$72.27

$74.88

$73.08

$78.48

$77.73

$73.32

$33.32

$33.19

5$58.67

$58.96

$60.64

$62.60

$63.25

$61.71

$64.81

$58.81

$55.32

$55.96

$54.88

$52.39

$49.93

$52.72

$53.14

$52.96

$57.69

$56.42

$16.42

$16.35

-We used the FV, to find the value of our team’s stock option on the option’s start date (PV).

rtFVePV

rtFVePV rtFVePV

rtFVePV

rtFVePV

rtFVePV

rtFVePV where r is the weekly annual rate

t is the amount of time or weeks

)1700023.0(94.18 ePV …………………

In conclusion, after running the simulation, the expected present value of our option on the start day should be approximately $18.83. This value is pretty accurate considering that we used 6,000 simulations, average the present values 30 times, and then averaged the averages.

Even looking at the further exploration, changes in the risk-free rate and option length don’t make a significant difference.

For some further exploration, we considered the effects of the strike price, the length of the option, and the risk-free rate.

Our Values Stike Price     Risk-Free Rate Option Length

Normal   Decreased to $20 Increased to $60 Increased to 5% Increased to 25 wks

E(FV) E(PV) E(FV) E(PV) E(FV) E(PV) E(FV) E(PV) E(FV) E(PV)

$18.90 $18.83 $38.92 $38.77 $2.87 $2.86 $18.92 $18.61 $19.06 $18.99

Difference $20.02 $19.94 $16.03 $15.97 $0.02 $0.22 $0.16 $0.16