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, 2010 at 5:11am
Hi Maggie, yes, this formula only works for European options without dividends.
Peter.
Maggie March 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
Peter August 30th, 2009 at 5:11am
Yes, base price = stock (or futures) price.
vishnu August 29th, 2009 at 12:05am
base price means stock price or other
Joe June 17th, 2009 at 3:15am
How do you determine the volatitity?
Peter March 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.
saurabh March 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
please comment
Peter March 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.
saurabh March 25th, 2009 at 1:38am
or how do we use this to find out the strike price we add this to present market price???
saurabh March 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
Add a Comment