If an option went down in value, how much is due to theta decay and how much due to fall in IV

Question

Let us say that there was a stock trading at 100 and the 105 call was trading at 3 $. with 1 month to go

Now stock went up to 104 after 15 days, and the call dropped to 2.80 $, to the call buyer's dismay.

Now, I understand that this 20 cent drop is partly due to theta decay and partly due to fall in IV that corresponds to a rise in the stock price.

Is there a thumb rule to approximate what is the effect of theta and what is the effect of IV?

In this time period, let us assume that theta went from 5 cents/day to 8 cents/day. IV went from 50% to 30%. Vega stayed constant at .01.

Please excuse me if these numbers are not realistic. Feel free to put in more realistic numbers for the greeks and IV, given the option price.

Answer 1

Because there are several non-linearities involved this depends very much on where you are concerning the level of volatility and time to expiry. But I think what you really want is to get some feel for the sensitivities involved, right?

With the following demonstration you can play with all kinds of combinations of all parameters to get some intuition for the greeks (I preselected volatility and time to expiry to give you the idea):

You can find it here: http://demonstrations.wolfram.com/ExploringTheBlackScholesFormula/

If you are an Mathematica user you can also download the full code for this here: http://demonstrations.wolfram.com/downloadauthornb.cgi?name=ExploringTheBlackScholesFormula