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HP 17Bii, HP 17Bii+ and 19Bii Calculator - Black Scholes Equation

Black-Scholes Option Valuation
The equation in this document uses the theoretical model developed by Fisher Black and Myron Scholes to estimate the value of options to buy or sell financial assets.
The BLK.SCHLS equation estimates the value of a call or put option. One of the variables in this equation is the standard deviation of the rates of return on the stock. This number is not commonly available. However, the value may be estimated by using one of the following:
  • A source that publishes Beta statistics for a stock may also publish the standard deviation (or variance, which is the standard deviation squared) of the stock.
  • A sequence of stock prices at uniform time intervals can be used in the SD.ROR equation, explained later in this document, to calculate the sample standard deviation of the rates of return.
Entering and using the BLK.SCHLS equation
  note:
You will need approximately 2500 bytes of calculator memory to enter the BLK.SCHLS equation.
  1. Enter the following BLK.SCHLS equation into the Solver. Enter every character shown, except for spaces. All spacing is for readability. Do not enter any spaces into the calculator.
  2. Display the BLK.SCHLS equation menu.
  3. Store the following variables:
    • Stock price per share in {PS}.
    • Exercise price of option in {PE}.
    • Periodic risk free rate of return as a percentage in {RF%}.
    • Number of periods until expiration in {T}.
    • Standard deviation, as a decimal, of the periodic returns of the stock in {S}.
  4. Press CALLV to calculate the call option value per share of stock.
  5. Press PUTV to calculate the put option value per share of stock.
      note:
    The time units for RF%, T and S must be the same. For example, if S (standard deviation) is based on monthly rates of returns, then RF%(the risk free rate) and T (time until expiration) must also be expressed in months.
Example of entering and using the BLK.SCHLS equation
A call option on a stock has an exercise price of 45 and a current price of 52. The standard deviation of monthly rates of return for the stock is .2054, and the monthly T-Bill rate is .5%. The option expires in six months. What is the estimated value of the call?
Display the BLK.SCHLS equation menu.
Keys
Display
Description
52, then PS
PS=52.00
Stores current stock price.
45, then PE
PE=45.00
Stores exercise price.
.5, then RF%
RF%=0.50
Stores the risk free rate of return.
6, then T
T=6.00
Stores time period.
.2054, S, then MORE
S=0.21
Stores standard deviation of stock rates of return.
CALLV
CALLV=14.24
Calculates value of call option per share of stock.
PUTV
PUTV=5.91
Calculates value of put option per share of stock.
Standard deviation of rates of return
The variable S in the BLK.SCHLS equation is the standard deviation of the periodic rates of return of the stock. A sequence of stock prices at uniform time intervals can be used in the SD.ROR equation below to calcuate the sample standard deviation of the rates of return.
  note:
The equation does not include dividends, which is appropriate if the stock pays either a constant dividend or zero dividend over the period of time that the prices are measured.
Entering and using the SD.ROR equation
The steps for entering and using the SD.ROR equation are shown below:
  1. Enter the the following SD.ROR equation into the Solver. Enter every character shown, except for spaces. All spacing is for readability. Do not enter any spaces into the calculator.
  2. Enter the stock prices into a SUM list and name the list PRICE.
  3. Display the SD.ROR equation menu.
  4. Press {S} to calculate the standard deviation of the rates of return of the stock. (You may have to press {S} twice, since the first time you press it the machine may store the value in the display. Pressing {S} a second time will begin the solve calculation.)
Example of entering and using the SD.ROR equation
You have tracked the monthly closing stock prices of a corporation for 61 months. Calculate the sample standard deviaiton of returns for this set of prices.
Month
Price
1
42.000
2
39.875
3
39.750
4
37.875
5
37.375
6
37.875
7
41.750
8
43.125
9
40.375
10
42.750
11
46.625
12
47.625
13
50.125
14
55.000
15
49.125
16
54.875
17
62.750
18
61.500
19
63.875
20
62.625
Month
Price
21
57.875
22
63.750
23
67.125
24
68.250
25
64.875
26
61.750
27
63.000
28
63.000
29
65.125
30
56.875
31
57.000
32
52.375
33
49.375
34
52.000
35
57.750
36
60.625
37
61.250
38
64.875
39
67.000
40
75.000
Month
Price
41
78.250
42
75.125
43
82.375
44
87.500
45
90.500
46
99.500
47
117.000
48
115.000
49
118.125
50
113.875
51
116.375
52
114.375
53
114.625
54
116.125
55
125.875
56
120.125
57
136.125
58
123.625
59
129.125
60
124.250
61
129.250
  note:
The solution below assumes that you have the numbers above stored in a SUM or STAT list, named PRICE. As a check, the total of the list should be 4,512.88.
Display the SD.ROR equation menu. Then proceed to the following keystrokes to complete the calculations:
Keys
Display
Description
{S} {S}
S=0.07
Calculates sample standard deviation of the numbers in the SUM list named PRICE.
(SHIFT) SHOW
6.59623655232E-2
Shows result to full precision.
Further information
  note:
One or more of the above Web sites will take you outside of the Hewlett-Packard Web site. HP does not control and is not responsible for information outside of its Web site.

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