How to read Theta value in this example

[Derrenoption]

Hello,

I am looking at the 30 DTE ATM option in MSFT today.

I have inserted the values in this calculator:
http://www.bilddump.se/bilder/20161021232224-195.252.32.111.png

As seen we can read the PUT value:
11.37

What does that mean in this case. The PUT option price is at:
1.80

How much does this option loose per day?

When looking in TOS, I can see a value like this:
-0.03

I beleive that 11.37 means % like this:
Theta: 0.1137 * 1.80 = 0,20466

The option looses: 0.20466 in value per day?

 

[stepandfetchit]

First, you should try an apples to apples comparison: There are NO 30DTE options on MSFT today. There is a 28DTE and a 35DTE. Pick one, and change the calculator inputs to match. Also, you need to supply the correct Volatility to the calculator, so just plug in the one from TOS if you don't have a better value. Since the Calculator does not accommodate Dividends, you will encounter error unless you address this. (you can modify your underlying price from Spot price to (Spot price - PVDiv), where PVDiv is the present value of the Dividend which occurs during the contract.) -- I think this should be a close approximation);

Also the png for the calculator seems off: This one seems to work: "http://www.fintools.com/resources/online-calculators/options-calcs/options-calculator/"

 

[Doobs789]

Theta is an option's sensitivity time, so yes, decay. The 11.37 value is theta*100, raw theta would be 0.1137. Therefore, it will be worth 1.80 - 0.1137 = 1.68 in one day.

 

[stepandfetchit]

BTW: The accuracy of the greeks, theta, vega, .... is related to the accuracy of the IV used. A little error can go a very long way! ;-)

 

[Doobs789]

If you knew what the accurate IV was, then options wouldn't exist. You have to input something, either vol/price.

 

[stepandfetchit]

If you knew what the accurate IV was, then options wouldn't exist. You have to input something, either vol/price.

I don't understand your statement.
IV is the "unknown" variable to the BS Model. We can know all other inputs with varying amounts of precision.
Typically, IV is solved by differing methods (kinda depends on the accuracy required for whatever the user is trying to accomplish). Some people guess wildly at the IV value, and may merely use the Historical Volatility of the underlying. In cases like this, the Greeks derived, such as Theta may have excessive error. I was merely pointing out that if little care is use in choosing the IV, then you reap what you sow. -- Perhaps I could have worded this better.
I think the OP plans to use BSM and input all the known variables (Div yield, Interest rate, Spot price, Strike, Call/Put), then insure the IV results in the resulting price precisely match the Mid-Price of the specific Option. This is a good approximation of IV.

 

[Doobs789]

Yes, theo = mid of b/a. Input the price to derive the vol.

I think the OP was trying to understand what his theta value meant, not that it was inaccurate.

 

[JackRab]

That theta is wrong... it should be around 3 cents for the put... about the same for the call

But as @Doobs789 mentions, it probably is theta per 1 options of 100 underlying value.

So, you buy 1 put, costs 1.80 * 100 = 1800 dollars. Next day you've lost 11.37 dollars in theta...

But again, that theta is way off...
(Tip: for the ATM options, the theta is roughly: options price / 2x DTE)

EDIT: weird... 11.37 / 0.031 (my theta value) = about 365... so looks like it's multiplied by 1 year....

 

[Derrenoption]

I think the OP was trying to understand what his theta value meant, not that it was inaccurate.

Yes, it is something strange. I tried again with new values for the below PUT option:

Symbol: MSFT
Expiration: 18 Nov 2016

dividendyield = 0.0241;
riskfreerate = 0.0024;
stockprice = 59.66;
strikeprice = 60;
yearsexpiration = (double)26 / (double)365;
knownoptionprice = (1.38+1.42) / 2;

Then I get the value: 8.837. If we divide that by 100, we get: -0.08837
When looking in TOS, I can see a value of: -0.02

I use the C# code for theta from this class to return Theta:
http://www.risk256.com/code/Options.cs

I have also manually myself calculated the Theta value using the formula for Theta on this URL and I get exactly the same value from that calculation: -0.08837
http://www.wilmottwiki.com/wiki/index.php?title=Put_option

This one seems to work: "http://www.fintools.com/resources/online-calculators/options-calcs/options-calculator/"

That is true, this calculator shows: -0.024 which seems correct!

I am not sure why I get so wrong theta value with both my approaches and what could be wrong or what formula to use?

 

[JackRab]

That is true, this calculator shows: -0.024 which seems correct!

I am not sure why I get so wrong theta value with both my approaches and what could be wrong or what formula to use?

Again, 365*0.024 = 8.8... so maybe there's a miss in the calculations... or it uses some yearly value.

You can always double check by using the same values to calculate the option price, but in your MSFT example use 26 days and then 25 days... the difference is Theta.