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

2018-10-19 05:01:15

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 stochasti

• 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.

2018-10-19 05:09:47