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Explanation of Black-Scholes Option Valuation Equation
LAKSHMAN PURIHELLA, Member
The main equation for the Black-Scholes Option Valuation is as follows:
C = S.N(d1. - X.e-RT. N(d2. (12)
where:
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
+ +. 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...
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