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## Black-Scholes Model

The Black-Scholes Model is a mathematical formula designed to price an option. It is a function of a number of variables such as stock price, striking price, volatility, time to expiration, dividends to be paid, and the current risk-free interest rate. It is a fairly common method of option pricing but does use some assumptions which give rise to limitations. The main assumptions of the Black-Scholes Model are;

Although the **Black-Scholes Model** has these limitations compared to other more complex option pricing models, it is still popular with
option traders due to it's relative simplicity. For those of you who are mathematically inclined the Black-Scholes formula is as follows;

C_{0}= S_{0}N(d_{1}) - Xe^{-rT}N(d_{2})

Where:

d_{1}= [ln(S_{0}/X) + (r + σ^{2}/2)T]/ σ √T

And:

d_{2}= d_{1}- σ √T

And where:

C_{0}= current option value

S_{0}= current stock price

N(d) = the probability that a random draw from a standard normal distribution will be less than (d).

X = exercise price

e = 2.71828, the base of the natural log function

r = risk-free interest rate (usually the money market rate for a maturity equal to the option's maturity.)

T = time to option's maturity, in years

ln = natural logarithm function

σ = standard deviation of the annualized continuously compounded rate of return on the stock

## What to do if you need more help

If you need more help with your specific commercial loan, mortgage or insurance requirement please speak to a professional financial adviser.

We hope you found this information useful.

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