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Sunday, September 21, 2014 4:11:35 PM
Valuing Warrants with the Black-Scholes Model
Although there are several possible methods for valuing a warrant, a modified version of the Black-Scholes model is most common. This formula is for European-style options and, though American-style options are theoretically worth more, there is not much difference in price in practice.
In the Black-Scholes model, the valuation of a call option is expressed as:
C = S N(d1) - X e-rT N(d2)
Where:
C = price of the call option
S = price of the underlying stock
X = option exercise price
r = risk-free rate
T = time until expiration
N() = area under the normal curve
d1 = [ ln(S/X) + (r + s2/2) T ] / s T1/2
d2 = d1 - s T1/2
Because of the dilution that warrants represent, the value of that call needs to be divided by (1 + q) where q is the ratio of warrants to outstanding shares, assuming each warrant is worth one share.
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