Theta Decay - Intraday

Discussion in 'Options' started by rivercode, Aug 11, 2008.

  1. How is Theta decay intraday calculated ?

    From my understanding (pls correct me where I am wrong)...

    The existing theoretical models for pricing options are based on the number of days to expiration, so how do you calculate the intra-day value of a decaying option.

    How do Market Makers handle this ? Do they just adjust the Implied Volatility down during the day or are using a variation on the theoretical models that incorporates intraday decay ?
  2. dmo


    Models are actually based on years and fractions of years until expiration. If an options calculator asks you for days to expiration, it then divides the number you feed it by 365, and feeds the result to the pricing model. If you take minutes to expiration and divide it by minutes in a year, you can input the result into your pricing model directly. That's actually how the VIX is calculated (although the VIX is not calculated using a pricing model - they go about it a little differently).

    I personally never saw the need for such precision (minutes to expiration rather than days to expiration), but I'm sure there are firms that do it that way.
  3. Hi Rivercode,

    The most part of the models used in finance are based on the relationship between time and variance. (variance is the square of volatility). So, the more time you got, the more variance you got. Intuitively, it means the more time you have got the more an asset could have a great deviation (on square root scale).

    If the asset doesn't move, the option will change by the theta with time, ceteris paribus.( very very very strong assumption)

    Time decay=interest received on cash equivalent of portfolio value-(0,5*variance*square of asset value*gamma)

    Talking about intraday Theta decay is then linked with talking about intraday variance changes, that means you would never know exactly whether you are earning a theta decay or a decrease on volatility. (Sure you already witness an increase of volatility that vanishes time decay).

    Remember,"If the asset doesn't move, the option will change by the theta with time, ceteris paribus". But if an asset doesn't move you will witness a volatility drop.

    "How do Market Makers handle this ? Do they just adjust the Implied Volatility down during the day"
    that what I think is correct and how I take it on my positions.

    Best regards
  4. Thinking in terms of variance rather than in terms of time and volalitity is indeed is much better way to explain and grasp option premiums (what is the plural of premimum?), and not to fall in mis-interpretations.

    I have read a lot of posts and heard many times people saying that they have hard time understanding volatility.

    If explained in terms of variance, it is easier. For instance, for ATM (ATM defined with respect to forward price), one can understand many things by thinking that one is trading an instrument which is an increasing function of one variable (instead of two): the standard deviation. So a double of implied volatility can be thought of as a quadrupling of time (even if time cannot be rolled back it gives one a sense of the effect). And of course a reduction of vol to half the value can be tought of as cutting the time by 4.

    When I explain it this way to some people, they all of a sudden become "experts" at designing great spread.

    Try it with a shrewed businessman, and you will see what I mean.

    Also a lot of people lose money in earning annoucements because they do not think in terms of variance (combination of time and vol).