How to calculate natural Log?in option pricing model - Black Scholes Model
How to calculate natural log?in option pricing model - black
Anoop kumar (Article) (570 Points)
24 October 2012
6 Replies
Tehsinkhan Pathan
(CA CMA DISA(ICAI) B.COM)
(3956 Points)
Replied 24 October 2012
There are Three methods of calculation of value of Natural Log :-
(a) Using Natural log table
(b) Using ex/e-x table
(c) Using ordinary log tables
I Method: Using Natural log tables
Example 1 : Find the natural log of (a) 0.75 (b) 1.24 (c) 1.0379 (d) 1.2667
Answer
(a) ln(0.75) = -0.2877
(b) ln(1.24) = 0.2151
(c) ln(1.0379) =?
ln(1.03) = 0.0296
ln(1.04) = 0.0392
For LHS diff. of 0.01, RHS diff. is 0.0096
For LHS diff. of 1, RHS diff. is 0.96
For LHS diff. of 0.0079, RHS diff. is:
(0.96)x 0.0079 i.e. 0.0076
ln (1.0379) = 0.0296 +0.0076 = 0.03702
(d) ln(1.2667) =?
ln(1.26) = 0.2311
ln(1.27) = 0.2390
For LHS diff. of 0.01, RHS diff. is 0.0079
For LHS diff. of 1, RHS diff. is 0.79
For LHS diff. of 0.0067, RHS diff. is :
(0.79)x 0.0067 i.e. 0.005293
ln (1.2667) = 0.2311 + 0.005293 = 0.236393
Tehsinkhan Pathan
(CA CMA DISA(ICAI) B.COM)
(3956 Points)
Replied 24 October 2012
II Method: Using ex/e-x table
Let ex = y
then, ln(y) =x
Example 2 :
Find natural log of (i) 0.2567(ii) 0.3570 (iii)0.2466 (iv) 0.1979 and (v) 4.0960
Answers
(i) Consulting the table of values of ex/ e-x, we find :
0.2567 = e-1.36
Hence, natural log of 0.2567 = -1.36
(ii) Consulting the table of values of ex/e-x, we find :
0.3570 = e-1.03
Hence, natural log of 0.3570 = -1.03
(iii) Consulting the table of values of ex/e-x, we find :
0.2466 = e-1.40
Hence, natural log of 0.2466 = -1.40
(iv) Consulting the table of values of ex/e-x, we find :
0.1979 = e-1.62
Hence, natural log of 0.1979 = -1.62
(v) Consulting the table of values of ex/e-x, we find :
4.0960 = e1.41
Hence, natural log of 4.0960 = 1.41
Example 3 : Find the natural log of (a) 0.75 (b) 1.24 using ex/e-x table
Answer
(a) ln(0.75) = ?
e-0.28 = 0.7558
e-0.29 = 0.7483
0.7558 = e-0.28
0.7483 = e-0.29
For 0.0075 ↓ in LHS, e’s power ↓ by 0.01
For 1↓ in LHS, e’s power ↓ by 0.01/0.0075
For 0.0058 ↓ in LHS, e’s power ↓ by (0.01/0.0075)x0.0058 i.e. by 0.0077
= 0.7558 – 0.0058 = e-0.28-0.0077
0.75 = e-0.287686
ln 0.75 = -0.287686
(b) ln(1.24) = ?
e0.21 = 1.2337
e0.22 = 1.2461
1.2337 = e0.21
1.2461 = e0.22
For 0.0124 ↑ in LHS, e’s power ↑ by 0.01
For 1 ↑ in RHS, e’s power ↑ by 0.01/0.0124
For 0.0063 ↑ in RHS, e’s power ↑ by
(0.01/0.0124)x0.0063 i.e. 0.0050806
1.2337 +0.0063 = e0.21+0.0050806
= 1.24 = e0.215097
ln 1.24 = 0.215097
Tehsinkhan Pathan
(CA CMA DISA(ICAI) B.COM)
(3956 Points)
Replied 24 October 2012
III METHOD :- USING ORDINARY LOG TABLES
II Method: Using ex/e-x table
Read more at: /forum/how-to-calculate-natural-log-in-option-pricing-model-black-225325.asp#.UIgNve_P1Yg
Read more at: /forum/how-to-calculate-natural-log-in-option-pricing-model-black-225325.asp#.UIgNve_P1Yg
II Method: Using ex/e-x table
Read more at: /forum/how-to-calculate-natural-log-in-option-pricing-model-black-225325.asp#.UIgNve_P1Yg
Read more at: /forum/how-to-calculate-natural-log-in-option-pricing-model-black-225325.asp#.UIgNve_P1Yg
ln (x) i.e. natural log = Ordinary log of x / 0.4343
Example 4: Try Example 1 using ordinary log tables
Answer
(a) : ln(0.75) = ?
Log 0.75 = -0.1249
ln 0.75 = -0.1249/0.4343 = -0.2876
(b) ln(1.24) = ?
Log 1.24 = 0.0934
ln 1.24 = 0.0934/ .4343 = 0.2151
(c) ln(1.0379) =?
Log 1.0379 = Log 1.038 = 0.0162
ln 1.0379 = 0.0162/0.4343 = 0.0373
(d) ln(1.2667) = ?
Log 1.2667 = Log 1.267 = 0.1028
ln 1.2667 = 0.1028 / 0.4343 = 0.2367
Tehsinkhan Pathan
(CA CMA DISA(ICAI) B.COM)
(3956 Points)
Replied 24 October 2012
Follow the link below it may be helpful to you :-
Prachi Srivastava
(Finance)
(368 Points)
Replied 03 April 2014
Hi,
I am reading this post after approx 1 Year it was posted. It was of great help to me. Also please help in the following:-
1. How do I solve-- A=P(1+R/100)^23
2. Is there any book which I should refer to while preparing for Advance financial Management for Grp III of ICWAI.
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