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A Quick At-the-Money Option Price Approximation

Article Quant Q&A · Author: Sithered
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Summary

The document gives an interview-style question about estimating a European option price without a calculator and points to a simple approximation for at-the-money calls and puts: about 0.4 times the underlying price, volatility, and the square root of time to expiry. This provides a mental estimate when evaluating options under the stated conditions.

The note offers no derivation, numerical example, or comparison with an exact Black–Scholes price. The approximation is specifically framed for at-the-money options, so it should not be treated as a general pricing rule for options with other strikes or conditions. A second answer refers readers to another approximation resource but does not explain its method.

Key ideas

  • For an at-the-money call or put, a quick estimate is 0.4 times spot price, volatility, and the square root of time to expiry.
  • The approximation is intended for mental calculation when a calculator is unavailable.
  • The document does not establish the approximation's accuracy or extend it to options away from at the money.

Tags

OptionsDerivatives pricingVolatility
Full text
# Estimate simple option price without a calculator


# Estimate simple option price without a calculator












I have been to two different interviews for jobs related to option trading, and both time I have been asked a question, which is pretty basic, and still I could not answer it.

If you have an European call option, with :











What is its price? I could not use the BS formula, because I have no calculator. I think I should probably have used a binomial tree, but I didn't find out how.

Thank you for your help

## Answer by q.t.f. (score 7, accepted)

https://quant.stackexchange.com/a/17880

There is a good quick well-known approximation for at-the-money options: $$\textrm{Call,Put} = 0.4 S \sigma \sqrt{T}.$$ See further discussion at What are some useful approximations to the Black-Scholes formula?.

## Answer by Donald Harding (score 2)

https://quant.stackexchange.com/a/17896

I think that you can find the answer to this question here:

http://people.stern.nyu.edu/wsilber/chuang-silber%20approx%20option%20value.pdf

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.