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oBSw( ) Model Definition

The Black-Scholes closed-form warrant pricing formula is defined as follows:

Equation Template


Equation Template


W = warrant price

S = spot price of the underlying instrument.

X = exercise price (strike)

N = total number of outstanding shares of the underlying instrument.

M = the number of warrants

Equation Template= the number of shares that can be purchased with each warrant.

r = risk-free interest rate, expressed with continuous compounding

vol = standard deviation of the return of the spot price plus the diluted warrant price, i.e., S + (M/N)W

T = time to maturity measured in years (actual/365 basis)

N(.) = cumulative normal distribution of (.)

ti = time until the i'th dividend is paid.

Di = the dollar amount (per share ) of the i'th dividend.


As warrant price is a function of itself , an iteration procedure is used to determine the warrant price. That is, the outputted warrant price is compared against the inputted warrant price (which in the first instance is zero, and for all other instances is the outputted warrant price of the previous iteration). The iteration procedure continues until the outputted warrant price is within 15 decimal places of the inputted warrant price.


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