— delta — relation to current asset price, assuming out-of-the-money —
Assuming a call with strike above current asset price, out of the money, call premium rises along with current asset price . It feels like becoming more volatile/dangerous. Dangerous to the insurer.
 insurers make sure most of the time they don’t have to pay the claim
Assuming a put with strike below current asset price, out of the money, put (insurance) premium drops when current asset price moves higher and AWAY from strike price.
For out-of-the-money options, both call and put, when asset price moves closer to strike price, insurance premium escalates.
– A put writer (insurer) guarantees to buy our asset at a sky-high strike price. The insurer wishes asset MV to appreciate, so a depreciating MV means higher risk, higher premium.
– A call insurer wishes asset (eg oil) to depreciate, so an appreciating asset means higher risk, higher premium.
 Same thing if the call is in deep the money. Rising asset price further protects the buyer because the call is almost guaranteed to be in the money at expiration
— vvvvv vega — relation to vvvvvvol —
Vol increases option payoff; Vol makes options more PROFITABLE, as it’s more likely to hit the strike price. Stable securities have lower “insurance-premium”, as strike is disaster for the insurer.
Q: But what if the option we hold is already in-the-money? I read that higher vol always increases our valuation, but higher vol would increase the chance of going out-of-the-money?
A: I feel in this case high vol’s positive impact outweighs that particular negative impact. Positive impact is the increased chance of sky-high payoff.
— relation to strike price —
call valuation (ie insurance premium) drops with higher strike price, because it requires more volatility to hit it.
call valuation rises with lower strike price, because the strike is dangerously close to current price. As if more volatile.
put valuation drops with lower strike price. If you exercise, you sell the asset for less money — The simplest explanation.
put valuation rises with higher strike price. If you exercise, you sell the asset for more money — The simplest explanation.
— ttttt theta — relation to tttttime-to-expiration — decay of option valuation
For both calls and puts, longer time frame increases insurance premium, as asset has more “opportunities” to hit strike price.
If we hold a call or a put option, each day’s passage decreases our market value, AS IF vol drops.