There are various ways to calculate the price of a call option using the Black-Scholes model. Below is a spreadsheet that breaks the required formulas into pieces to make it easy to work with. Column (1) shows the various inputs. The first five cells are the required inputs for a non-dividend paying stock. The remainder of the cells are the formula parts. Column (2) shows a solved problem for a stock selling for $50, with an exercise price of $45, an interest rate of 6 percent, 90 days (one-quarter of a year), and a standard deviation of .235. Column (3) shows how the cell values in Column (2) were calculated. Once you have this set up in the spreadsheet, you can calculate the price of any call option by substituting the correct values in the first five cells of column (2). Spreadsheet begins in row 2. Calculating a Call Price Using the Black-Scholes Model 50 45 R 0.06 T 0.25 0.235 In(S/X) 0.105361 LN(B2/B3) r+0.50? 0.087613 B4+(,5)*(B6)^2 o(t)½ 0.1175 B6*((B5)^0.5) IP d2 1.083095 (B7+(B8*B5))/B9 0.965595 BIO-B9 N(dI) 0.860617 NORMSDIST(BI0) N(d2) 0.832877 NORMSDIST(BI I) S*N(d1) 43.03084 B2*B12 E 2.7183 -rt e 0.985 |12 B15^-(B4*B5) Call Price 6.109398 B14-(B3*B16*BI3)
There are various ways to calculate the price of a call option using the Black-Scholes model. Below is a spreadsheet that breaks the required formulas into pieces to make it easy to work with. Column (1) shows the various inputs. The first five cells are the required inputs for a non-dividend paying stock. The remainder of the cells are the formula parts. Column (2) shows a solved problem for a stock selling for $50, with an exercise price of $45, an interest rate of 6 percent, 90 days (one-quarter of a year), and a standard deviation of .235. Column (3) shows how the cell values in Column (2) were calculated. Once you have this set up in the spreadsheet, you can calculate the price of any call option by substituting the correct values in the first five cells of column (2). Spreadsheet begins in row 2. Calculating a Call Price Using the Black-Scholes Model 50 45 R 0.06 T 0.25 0.235 In(S/X) 0.105361 LN(B2/B3) r+0.50? 0.087613 B4+(,5)*(B6)^2 o(t)½ 0.1175 B6*((B5)^0.5) IP d2 1.083095 (B7+(B8*B5))/B9 0.965595 BIO-B9 N(dI) 0.860617 NORMSDIST(BI0) N(d2) 0.832877 NORMSDIST(BI I) S*N(d1) 43.03084 B2*B12 E 2.7183 -rt e 0.985 |12 B15^-(B4*B5) Call Price 6.109398 B14-(B3*B16*BI3)
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Transcribed Image Text:There are various ways to calculate the price of a call option using the Black-Scholes model.
Below is a spreadsheet that breaks the required formulas into pieces to make it easy to work
with. Column (1) shows the various inputs. The first five cells are the required inputs for a
non-dividend paying stock. The remainder of the cells are the formula parts. Column (2)
shows a solved problem for a stock selling for $50, with an exercise price of $45, an interest
rate of 6 percent, 90 days (one-quarter of a year), and a standard deviation of .235. Column
(3) shows how the cell values in Column (2) were calculated.
Once you have this set up in the spreadsheet, you can calculate the price of any call
option by substituting the correct values in the first five cells of column (2). Spreadsheet
begins in row 2.
Calculating a Call Price Using the Black-Scholes Model
S
50
45
R
0.06
T
0.25
S
0.235
In(S/X)
0.105361
LN(B2/B3)
r+0.50?
0.087613
B4+(,5)*(B6)^2
o(t)½
0.1175
В6*((B5)^0.5)
dl
1.083095
(B7+(B8*B5))/B9
d2
0.965595
BIO-B9
N(d1)
0.860617
NORMSDIST(BI0)
N(d2)
0.832877
NORMSDIST(BI )
S*N(d1)
43.03084
B2*B12
E
2.7183
-rt
e
0.985112
BI5^-(B4*B5)
Call Price
6.109398
B14-(B3*B16*BI3)
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