# In option pricing formulas, is the volatility and short rate a decimal or a percentage?

In the BS option pricing formula, when entering values for volatility and short rate, do we enter them as percentages or decimals?

Take the time unit to be a year, i.e. if we want to price something a year from now, we'd let T = 1.

I am not just looking for an answer, but also an explanation. If the answer is decimal, then what goes wrong when I use percentage? What would I need to "fix" in order to be able to enter percentages? (apart from just multiplying the parameter with 100 in the formula!)

Note: BS above, stands for Black–Scholes model, a equation that reflects the value of a given option based on multiple variables that are input to the equation.

do we enter them as percentages or decimals?

As a decimal. A "20%" annualized volatility would be entered as 0.2 in the Black-Scholes model

I am not just looking for an answer, but also an explanation.

The fundamental assumption of the Black-Scholes model is that the underlying price is a stochastic process which has a standard deviation of `s` (omega in the actual formula). Since the time variable is expressed in years, `s` can be translated as the standard deviation of returns over 1 year.

If the answer is decimal, then what goes wrong when I use percentage?

Your volatility will be off by a factor or 100 and your option price will be extremely too high

What would I need to "fix" in order to be able to enter percentages?

I'm not certain what you mean - if you have a percentage (e.g. 20%) just divide it by 100 to use it in the Black-Scholes model.

• Which way would be computed values be off if the risk free rate of return was entered 100 times too big? Is that used to discount the different possible future values, and as such would cause the computed option value to be too small, or something else? Feb 24, 2017 at 23:53
• @ShannonSeverance As risk-free return increases, call prices will increase and put prices will decrease, although not by nearly the same magnitude as volatility being off by 100. Feb 24, 2017 at 23:55