Hot answers tagged theta
No because they are worthless in the first place. Theta is in dollar space and therefore, if something is worthless, it is hard for it to lose much more value. Think about it this way. When you are buying an option, you are really buying gamma from BS PDE. The cost of gamma is theta. Where is gamma highest? ATM
if you have a portfolio of calls and puts with the same maturity then your portfolio is gamma neutral if and only if it is vega neutral. The reasons is that the BS gamma divided by the BS vega is a function of $S$ and $T$ that does not vary with $K.$ So if you construct a linear combination that has zero gamma then the vega is zero too, and vice versa.
It's hard to be sure without seeing the inputs, but I'm guessing that the implied curve changes shape because the original curve does (which you can see from your output: except for the 1-year and 5-years points, the actual discounts are different). The reason the original curve changes is probably the different position of weekends or holidays (so that, ...
The value of a call option that is near ATM can be approximated as $C(S,T)≈ 0.4 \sigma \sqrt T$. Therefore, under the unrealistic assumption that S does not change very much (i.e. the option stays near the money) the value decays as the square root of the remaining time. In words, yes it does speed up considerably as you get close to expiration.
I don't understand why you think the numbers dont match up. In my opinion it all works out. Perhaps best if you first convert all numbers to percentages and for 1 underlying instead of 100 multiplier. From OVML you have multiplier = 1 troy ounce S = 1075 K = 1075 r = 0.0033 T = 2/12 sig = 0.12 Convert all into percentages: S = 100 K = 100 r = ...
I don't think your hypothesis is correct. If you have a very short dated ATM option, then your option will have close to infinite gamma but close to 0 vega. So this short dated ATM option is vega neutral but definitely not gamma neutral.
Disclaimer: I did not check your example, i.e., that "theta * 1 day" will predict a negative option price. Theta is the derivative with respect to time-to-maturity. It is the change of the option price with respect to an infinitessimal change in time and not with respect to a change of one day - even if the derivative is "scaled" towards a time scale having ...
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