Explanation of Black-Scholes Option Valuation Equation

Black-Scholes Model > Forum Log in

Explanation of Black-Scholes Option Valuation Equation
LAKSHMAN PURIHELLA, Accountant, Saudi Arabia

The main equation for the Black-Scholes Option Valuation is as follows:
C = S.N(d1. - X.e-RT. N(d2. (12)
C is the value of call option
S is the current market price of shares in question
X is the future exercise price
R is the risk free interest rate per annum
T is the time to expiry (in years)
e is the mathematical constant 2.718, used to calculate value on a continuous compounding basis.
(X.eRT is the future value or amount, at time T, of a sum of money X invested @ R% on continuous compounding basis. If compounded annually, the amount at R% compound rate of interest at time T is X(1 + r/100)T, which is roughly equal to X.eRT)
N(d1) and N(d2) represent the cumulative area under the normal distribution curve for a 'z'* value of d1 and d2 where
d1 = log(S / X) RT
+ +. V.T
d2= d1 V.T
And log (SIX) is the natural log (to the base 'e') of SIX.
*'z' is the standard normal variable (observation value) in a normal distribution with a mean (μ) = 0, and a standard deviation 6 = 1. The value of z is given by:
z = X − μ    (A)
X is a variable, which can take any value in a normal distribution.
The value of z reflects the deviation from the mean (vertical line drawn at the mean value 0 and hence determines the area under the curve between - z and + z.
Suppose a normal distribution has a mean (μ) of 10 and a standard deviation σ of 5. If we want to know the probability of x having a value between 0.2 and 19.8, we shall find z for x = 0.2 and x = 19.8 by using the formula (A). The value of z works out as - 1.96 and + 1.96, and for z = 1.96, the area under the normal curve is a 0.95 from the tables. There is thus 95% probability that x will have a value between 0.2 and 19.8.



  Do you wish to study further? You can learn more from the summary, forum, discussions, lessons, courses, training, instructions, expert tips, best practices and education sources. Register.  

Special Interest Group Leader

You here

More on Black-Scholes Model
Best Practices

Expert Tips


About 12manage | Advertising | Link to us | Privacy | Terms of Service
Copyright 2017 12manage - The Executive Fast Track. V14.1 - Last updated: 22-8-2017. All names tm by their owners.