# 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.

PeterJune 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.

mohitJune 17th, 2014 at 4:55am

How do you determine the volatitity?

PeterFebruary 11th, 2014 at 3:32am

Hi Manish, can you explain further please? What values did you use?

ManishJanuary 30th, 2014 at 4:19am

PeterDecember 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.

SandeepNovember 16th, 2013 at 7:56am

Hi,Peter,
If the time ratio is just days,then how to calculate.

andreasNovember 14th, 2013 at 4:29am

Also, formula only works if forward is flat, ie divs = R

AmitabhMarch 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.

PeterMarch 11th, 2012 at 7:45pm

Hi Amitabh,

Exploiting the difference between the theoretical price and the actual price of an option requires constant hedging of the option with the underlying instrument and becomes a bet on volatility.

The idea is that you've priced the option using a specific volatility value, which is assumed to be the volatility that the underlying will experience from the trade date until the expiration date.

This is not really a good strategy for the average retail trader as the relatively higher brokerage charges will eat up a lot of the potential profits. Also, volatility forecasting in itself is a tough subject to master.

AmitabhMarch 10th, 2012 at 12:40pm

Hi Peter,

thanks for sharing the sheets. Have a query here. This will assist in building a strategy.

E.g. EOD Nifty is 5333.55, Futures is 5364.15. 5300 PUT is at 97.2. Your "Basic" page gives 74. Market has gone bullish and there is 19 days to expiry.

You mentioned "by exploiting the difference between their traded price and the theoretical price of the option".

So how can this price difference(given above) be exploited? What should be the position for PUT.

Any input will certainly help.

PeterFebruary 5th, 2012 at 4:38pm

This is how option market makers make money in options - by exploiting the difference between their traded price and the theoretical price of the option.

amirFebruary 3rd, 2012 at 10:26pm

It is all rubbish.
The only way to win is by analyzing the historical data.

PeterAugust 12th, 2011 at 4:58am

SontyAugust 12th, 2011 at 3:48am

HI

This formula is work only for ATM of OTM money option. pl suggest how we can use this for ITM option and for specitic strike price

Investment Research ToolFebruary 24th, 2011 at 5:31am

ansFebruary 16th, 2011 at 11:23am

before you make any comments, please read PhilTheGreek's comment. This simple formula works only for ATM. So \$45 is the asset current spot price and also the strike price. Again, 0.4 is 1/sqrt(2*pi).

PeterAugust 29th, 2010 at 1:45am

No, but you can use an online version, like,

Option Calculator

raju jeeAugust 28th, 2010 at 11:47am

is there any simple java mobile application avalaible for option priceing?

PeterMarch 11th, 2010 at 5:11am

Hi Maggie, yes, this formula only works for European options without dividends.

Peter.

MaggieMarch 10th, 2010 at 12:04pm

If I have the the "u,d, possibility(p)" in binomial model, how can I get the volatility for BS? this is a bit academic. thanks

PeterAugust 30th, 2009 at 5:11am

Yes, base price = stock (or futures) price.

vishnuAugust 29th, 2009 at 12:05am

base price means stock price or other

JoeJune 17th, 2009 at 3:15am

How do you determine the volatitity?

PeterMarch 26th, 2009 at 5:40pm

The \$45 is the underlying stock price...not the market price of the option.

If the market price of the option was \$2 then it would be undervalued as the theoretical is higher then what it is trading for in the market.

saurabhMarch 25th, 2009 at 11:07pm

Thanks Peter.
please correct me, if i am wrong.
Here Theoritical value is 2.07 and the market value is 45, it means that the option is overpriced?? (The market price of the option should be 2.07 but it is 45 actually

PeterMarch 25th, 2009 at 4:54am

Hi Saurabh,

The formula above only works for ATM options...not for a specific strike.

If you want a pricing model in Excel click on the Free Spreadsheet link above.

saurabhMarch 25th, 2009 at 1:38am

or how do we use this to find out the strike price we add this to present market price???

saurabhMarch 25th, 2009 at 1:34am

PLEASE explain me the meaning of this 2.07. how do we use this to find out ITM or OTM

It's because this is for calculating an ATM option. The strike price is the same as the base price.

ChrisJanuary 8th, 2009 at 5:30am

I don't see any mention of the Strike price.

PhilTheGreekSeptember 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).