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
Peter May 11th, 2022 at 2:27am
What were the other parameters that you used in your BS model inputs?
The quick pricer here is only an estimate btw.
Treasure May 10th, 2022 at 5:59am
I got a 28.81 market price when I use the BS model (from your spreadsheet) and I get 22.62 when I use the simplified pricing method. How do I explain this, please? Also, whats the key assumption of this simplified method?
Peter June 17th, 2014 at 7:23am
Hi Mohit,
You can use a volatility calculator to calculate the historical volatility or use your own view of what you think the volatility will be from trade date until the expiration date.
mohit June 17th, 2014 at 4:55am
How do you determine the volatitity?
Peter February 11th, 2014 at 3:32am
Hi Manish, can you explain further please? What values did you use?
Manish January 30th, 2014 at 4:19am
Not work your shortcut, please help me..........
Peter December 3rd, 2013 at 2:54am
Hi Sandeep,
The ratio includes the days - so if there are 30 days to expiration then "time ratio" is 30/365.
Sandeep November 16th, 2013 at 7:56am
Hi,Peter,
If the time ratio is just days,then how to calculate.
andreas November 14th, 2013 at 4:29am
Also, formula only works if forward is flat, ie divs = R
Amitabh March 12th, 2012 at 6:43am
Hi Peter
Brokerage factor is very correct.
Very interesting tool you have built. Have to note how this can be integrated with my existing setup.
Thanks for the inputs.
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