Why do higher and lower strike prices for options all go up when a stock tanks?
I am looking at Apple today (as an example), and with it down $8 today and currently at $376, why would the October options for both $365 and $395 skyrocket?
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There are two components of option valuation, the value that's "in the money" and the "time value." In the case of the $395 put, that option was already in the money and it will move less than the stock price by a bit as there will still be some time value there. $22.52 is intrinsic value (the right word for 'in the money') and the rest is time. The $365 strike is still out of the money, but as jldugger implied, the chance of it going through that strike is better as it's $6.66 closer.
Looking at the options chain gives you a better perspective on this. If Apple went up $20 Monday, and down $20 Tuesday, these prices would be higher as implied volatility would also go higher.
Now, I'd hardly call a drop of under 2% "tanking" but on the otherhand, I'd not call the 25% jump in the option price skyrocketing. Options do this all the time. Curious what prompted the question, are you interested in trading options? This stock in particular?
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.
Options pricing is based on the gap between strike and the current market, and volatility. That's why the VIX, a commonly accepted volatility index, is actually just a weighted blend of S&P 500 future options prices.
A general rise in the price of options indicates people don't know whether it will go up or down next, and are therefore less willing to take that risk.
But your question is why everything underwater in the puts chain went higher, and that's simple: now that Apple's down, the probability of falling a few more points is higher. Especially since Apple has gone through some recent rough times, and stocks in general are seen as risky these days.