Separating Option Theta Decay from Implied Volatility Effects
Summary
The question asks how to attribute an option price change between time decay and a change in implied volatility, using a call whose underlying rises while the option loses a small amount of value. It supplies hypothetical theta and vega figures, but the answer does not calculate an attribution or provide a rule of thumb. Instead, it emphasizes that the sensitivities are nonlinear and depend on volatility and time remaining until expiration.
The response recommends experimenting with a Black–Scholes demonstration to build intuition by changing model inputs, and notes that source code is available for users of a particular mathematical software package. This is a learning suggestion, not an empirical result or a complete decomposition method. It also leaves out the effect of the underlying price move and does not explain how to handle changing Greeks or interactions between inputs when measuring realized option P&L.
Key ideas
- An option price move cannot generally be divided into theta and volatility effects with one fixed rule.
- The sensitivities vary with the volatility level and time remaining to expiration.
- The response recommends exploring Black–Scholes inputs interactively to develop intuition.
- The answer does not perform the proposed attribution or account for the underlying price change.
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Full text
# If an option went down in value, how much is due to theta decay and how much due to fall in IV # If an option went down in value, how much is due to theta decay and how much due to fall in IV 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 by vonjd (score 3, accepted) https://quant.stackexchange.com/a/16771 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
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