Understanding the Straddle

Straddles are one of the most common option positions. A long straddle consists of being long both a call and put on the same strike in the same expiration. You are hoping the stock moves somewhere far away from the strike.
The value of a straddle, being composed of options, is determined by the level of volatility.
Volatility is simply the standard deviation of returns.
The value of a straddle:
  • is determined by the level of volatility
  • inverting — it can also be used to imply the level of volatility
If compound returns for a stock conform to a normal distribution and we have a reasonable estimate of the volatility we can use Black-Scholes to compute option prices and of course straddles.
This is the Black-Scholes formula for a European-style option assuming no dividends:
notion image
You know what’s more fun? Shortcuts.
You can get a very close approximation for a straddle price with the following formula:
ATF Straddle Approximation
notion image
S = forward price
σ = annualized volatility
t = fraction of a year until expiry
I think you’ll find this visual derivation of this approximation highly satisfying
Visual Derivation of Straddle Approximation