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The last couple of weeks we have been reviewing how changes in IV affects the greeks. So far we have covered delta and gamma. Today lets go over theta.
Theta measures time decay of an option. The theta number typically refers to how much the option will decay in one day’s time. So if I have an option with a theta of 22, that means the option theoretically will lose $22 of value today. Since options are decaying assets they will lose all their extrinsic value by expiration date and left only with their intrinsic value – 0 for all out of the money options and the difference between strike price and underlying for in the money options.
Theta only measures the erosion of extrinsic value or time value of the option. When IV goes up, extrinsic value increases – people bid up options independent of what the underlying is doing. It then follows that when there is more extrinsic value and all that extrinsic value must go to 0 by expiration, then the rate of decay or theta must increase. So the option we had that had a theta of 22 might now, with higher IV, have a theta of 30.
Conversely when vols are low and there is relatively little extrinsic value in the options, the daily rate of theta is lower since there is simply less extrinsic value to decay. Instead of 22 theta it might be 15. The main takeaway is simply if all extrinsic value disappears by expiration, as that extrinsic value move due to IV changes, the theta must also change accordingly.