# What does the theta curve of an american option look like?

Is the theta decay curve you see often given around the internet below in fact valid for American-style options? Often times, calculations for European-style options (Black-Scholes) are passed off as being valid for American-style options, so I wanted to make sure.

• That graphic isn't even accurate for OTM Europeans. Mar 16 at 7:44
• Under GBM, the variance of the price movement until maturity is proportional to $T$, so the standard deviation is proportional to $\sqrt{T}$. The value of an ATM option is also approximately proportional to this (see optiontradingtips.com/pricing/a-quick-pricer.html ). That is why they drew a "square root of time left" curve in the above graph. It is good enough qualitatively but does not consider Strike, interest rate, dividends, Americanness, etc. all of which are going to modify the curve somewhat. It is fine, but it is not a very detailed or accurate analysis. Mar 16 at 15:31