Black Scholes with Dividends

BSDOPM

BSDOPMTEXT

See also BSOPM

This function calculates the value of an option using the Black-Scholes Option Pricing Model on a dividend paying stock.

It also calculates a variety of other characteristics of the option

This function requires the user to supply the necessary inputs to the model

There is a companion function that labels the output. (BSDOPMTEXT)

The function can be used as either an array function or a single cell function

If using it as an array formula highlight 11 cell (either column or row) click on the formula bar and type the formula, and then press Shift-Control-Enter

Excel will supply the brackets around the formula.

If it is used as a single cell formula the user can enter an optional value which returns a particular value for the option

The companion formula BSOPTEXT behaves the same way. It returns a label for the output from the BSDOPM function and is provided for convenience in labeling the output.

Here are the inputs and form of the function:

=BSDOPM(S,E,T,STD,R,DIV,Optional Value,CC)

Example Inputs:

Row/Col

B

C

D

E

F

G

18

Inputs Required:

 

 

Example Values

 

19

DIV  is the Dividend Yield of the stock ($Dividend/$Stock Price)**

2.86%

 

20

S  is the current price of the stock

 

 

$14.00

 

21

E    is the call exercise price

 

 

$17.50

 

22

T   is time to expiration of the option in years

 

4

 

23

R    is the riskless, continuously compounded, interest rate

6.77%

 

24

STD is the Standard Deviation of the rate of return on which the option

30.83%

 

25

       is written

 

 

 

 

 

26

CC is optional and can be set to "yes" (Quotes required) and will convert R to continuous

 

27

      rate of return, if it was entered as a discrete rate

 

 

28

(**for convenience the function will convert Dividend yield to a continuous yield automatically)

 

29

 

 

 

 

 

 

30

To obtain:

Optional Value

 

 

 

31

Call Value

Default:  1

 

 

 

 

32

Put Value

2

 

33

Call Delta (Hedge Ratio)

3

There is no need to use these in the array form of the formula

 

 

 

34

Borrow/Lend $

4

 

 

 

35

Put Delta

5

 

 

 

36

Gamma

6

 

 

 

37

Vega

7

 

 

 

 

38

Call Theta

8

 

 

 

 

39

Put Theta

9

 

 

 

 

40

Call Rho

10

 

 

 

 

41

Put Rho

11

 

 

 

 

42

 

 

 

 

 

 

43

Delta: Is the impact on the option price of a change in the share price

 

 

44

Borrow/Lend: Amount necessary borrow/lend in replicating the option

 

 

45

Gamma: Is the impact on Delta of a price change in the share price

 

 

46

Vega: The impact on the option price for a change in the standard deviation

 

 

47

Theta: The impact on the option price for a small change in the time to maturity

 

48

Rho: The impact on the option price for a change in the risk free rate

 

 

49

 

 

 

 

 

 

50

Examples

 

 

 

 

 

51

Array function results:

Formula in cell to left

 

 

52

 

 

 

 

 

 

53

Call Value

2.715

{=BSDOPM(F20,F21,F22,F24,F23,F19)}

 

54

Put Value

3.577

{=BSDOPM(F20,F21,F22,F24,F23,F19)}

 

55

Call Delta (Hedge Ratio)

0.517

{=BSDOPM(F20,F21,F22,F24,F23,F19)}

 

56

Borrow/Lend $

4.519

{=BSDOPM(F20,F21,F22,F24,F23,F19)}

 

57

Put Delta

-0.375

{=BSDOPM(F20,F21,F22,F24,F23,F19)}

 

58

Gamma

0.051

{=BSDOPM(F20,F21,F22,F24,F23,F19)}

 

59

Vega

9.767

{=BSDOPM(F20,F21,F22,F24,F23,F19)}

 

60

Call Theta

-0.475

{=BSDOPM(F20,F21,F22,F24,F23,F19)}

 

61

Put Theta

0.071

{=BSDOPM(F20,F21,F22,F24,F23,F19)}

 

62

Call Rho

18.075

{=BSDOPM(F20,F21,F22,F24,F23,F19)}

 

63

Put Rho

-35.327

{=BSDOPM(F20,F21,F22,F24,F23,F19)}

 

64

 

 

 

 

 

65

The array formula in these cells is:

 

 

 

 

66

=BSDOPMtext()

 

 

 

 

 

67

 

 

 

68

You can choose to use the non-array form with same options as BSDOPM

 

 

 

 

 

69

 

 

 

 

 

70

 

 

 

 

 

71

 

 

 

 

 

 

72

Single Cell:

Formula in cell to left

 

 

73

 

 

 

 

 

 

74

Call Value

2.715

=BSDOPM(F20,F21,F22,F24,F23,F19)

 

75

Put Value

3.577

=BSDOPM(F20,F21,F22,F24,F23,F19,C32)

 

76

Call Delta (Hedge Ratio)

0.517

=BSDOPM(F20,F21,F22,F24,F23,F19,C33)

 

77

Borrow/Lend $

4.519

=BSDOPM(F20,F21,F22,F24,F23,F19,C34)

 

78

Put Delta

-0.375

=BSDOPM(F20,F21,F22,F24,F23,F19,C35)

 

79

Gamma

0.051

=BSDOPM(F20,F21,F22,F24,F23,F19,C36)

 

80

Vega

9.767

=BSDOPM(F20,F21,F22,F24,F23,F19,C37)

 

81

Call Theta

-0.475

=BSDOPM(F20,F21,F22,F24,F23,F19,C38)

 

82

Put Theta

0.071

=BSDOPM(F20,F21,F22,F24,F23,F19,C39)

 

83

Call Rho

18.075

=BSDOPM(F20,F21,F22,F24,F23,F19,C40)

 

84

Put Rho

-35.327

=BSDOPM(F20,F21,F22,F24,F23,F19,C41)

 

 

 

 

 

 

 

 

formula in cell b84 =bsdopmtext(C41)

 

 

 

 

[FinPak] [Getting FinPak] [Installation] [Help] [Fin Functions] [Simulation] [The Greeks] [Array Functions] [Root Finding]

Copyright 2003 Pieter A. Vandenberg All rights reserved.