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 March 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.
Amitabh March 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.
Peter February 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.
amir February 3rd, 2012 at 10:26pm
It is all rubbish.
The only way to win is by analyzing the historical data.
Peter August 12th, 2011 at 4:58am
Sure, try my option spreadsheet.
Sonty August 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 Tool February 24th, 2011 at 5:31am
These methods are really helpful in stock market trading.
ans February 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).
Peter August 29th, 2010 at 1:45am
No, but you can use an online version, like,
Option Calculator
raju jee August 28th, 2010 at 11:47am
is there any simple java mobile application avalaible for option priceing?
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