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Why do put option prices go higher when the underlying stock tanks (drops)?
When you buy a put on a stock, you buy the right to sell the stock at fixed price, F, that his usually different from the market price, M. You paid a price, P, for the put.  Your potential profit, going forward, is represented by the DIFFERENCE you get to collect between your fixed price F, and that market price M, plus the price you paid for the put, or F-(M+P). (This assumes that F>(M+P). P is fixed, but the smaller M gets, the larger the term F-(M+P), and therefore the higher your potential profit from owning the put. So when M "tanks," the put goes higher.  The $395 put is already in the money. If it were settled today, the value would be $395-$376 or $19. This, minus the cost of the put itself, represents your profit. The $365 put is "out of the money." The stock has to fall $11 more before the put is exercised. But if the stock went down 8 points today, that is less than the $19 difference at the start of the day. Because there is time between now and October, there is a chance for the stock to go down further, thereby going into the money. The current value of the put is represented by this "chance." Obviously, the chances of the stock going down $11 more (from today) is greater than the chance of it going down $19 more. On the other hand, the closer it gets to the expiration date, the less an out of the money put is worth. It's a race between the stock's fall, and the time to expiration.