How to Manually Price an Option
If you've no time for Black and Scholes and need a quick estimate for an at-the-money call or put option, here is a simple formula.
Price = (0.4 * Volatility * Square Root(Time Ratio)) * Base Price
Time ratio is the time in years that option has until expiration. So, for a 6 month option take the square root of 0.50 (half a year).
For example: calculate the price of an ATM option (call and put) that has 3 months until expiration. The underlying volatility is 23% and the current stock price is $45.
Answer: = 0.4 * 0.23 * SQRT(.25) * 45
Option Theoretical (approx) = 2.07
How Accurate is this Formula?
Let's take this formula and compare it to the Black and Scholes formula used in my option pricing spreadsheet.
| Stock | Volatility | Days | B&S | Manual | Difference |
|---|---|---|---|---|---|
| 10 | 35% | 229 | 1.10245 | 1.10892 | 0.00646 |
| 25 | 45% | 335 | 4.26664 | 4.3111 | 0.04447 |
| 50 | 25% | 52 | 1.88154 | 1.88723 | 0.00569 |
| 100 | 20% | 354 | 7.84501 | 7.87853 | 0.03352 |
Remember, this only works for ATM options, where ATM would be assumed to be the forward price of the underlying given the expiration date of the option; not the actual spot price.
34 Comments
Admin January 8th, 2009 at 3:32pm
It's because this is for calculating an ATM option. The strike price is the same as the base price.
Chris January 8th, 2009 at 5:30am
I don't see any mention of the Strike price.
PhilTheGreek September 14th, 2008 at 12:45am
This is a result from Black-Scholes equation S*N(d1)-K*N(d2) assuming zero interest rate and setting S=K, gives S*{N[+0.5*volatility*sqrt(time)]-N[-0.5*volatility*sqrt(time)]} which is S*volatility*sqrt(time)/sqrt(2*pi) and 0.4 is 1/sqrt(2*pi).
adrian September 4th, 2008 at 4:06pm
would the base price in this case be $45 ?
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