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As a dollar amount move of a percentage of stock price, do higher share priced stocks pay more on changes?


I noticed Google's price shifted $90 dollars and that the intrinsic value of a $500 call strike price, $50 above that day's start share price on earnings day, moved up from 10 cents to over $35 the next day! This all from a 18% move in stock price!

If this had been Sprint, making an 18% move, the option's intrinsic value would never have moved that much in dollars, would it?

Ten cents goes into 35 dollars 35000 percent?

If
(1) GOOG and S had the same implied volatility (IV)
(2) the options for each could be traded at their value, and
(3) the options for each were purchased the same percentage above the stock price, then
(1) the options for each will have the same percentage move in value, which in turn means
(a) an option for a higher priced stock will have a larger dollar move, but
(b) if the same amount is invested in each the number of dollars earned would be the same.

The problem is that none of the conditions given are true.

The first condition was "GOOG and S had the same implied volatility" which is not true. The IV for S is 72.07%. The IV for GOOG is 34.08% That will make the options for S more expensive. (Low priced stocks usually have lhigher IVs.)

The second condition was "the options for each could be traded at their value" which is also not true. A 10 cent option for a $449.54 stock is trading at 0.02% of the stock price. For an option to trade at 0.02% of a $6.48 stock it would have to trade for 0.14 cents. However, if you try to buy a call option on S the order will be rejected unless it is a multiple of 5 cents. So even though the option's value is only 0.14 cents, you cannot buy it at that price. (There are some circumstances where you can get option prices down to penny increments, but even at one cent you would be paying over seven times the options value to buy it.)

The third condition was "the options for each were purchased the same percentage above the stock price" which is also untrue. Options for S have strike prices $1.00 apart. One dollar is over 15% of the price for a $6.48 stock (as of Thursday's close). The strike prices for GOOG are every $10, about 2% of a $449.54 stock price.

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Finally, I cannot let some of the misinformation in the first answser to your question go uncorrected.

It said "Option pricing is most dependent on volatility. The higher a stock's volatility, the more expensive the option. Google is a more volatile stock than Sprint so its options will be more expensive."

The price of an option does not depend at all on the previous volatility of a stock. It depends, in part, on the "implied volatility" of the stock which is, in simplistic terms, the amount of future volatility expected in the stock until the option expires. It is also worth noting that if you go by Beta (which measures one year volatility) or historical volatility over the last 20 days (prior to Friday's trading) S was more volatile than GOOG.

The first answer also said "There are two components to an option price--the positive difference between the stock price and the option strike price and the time to expiration."

The value of an option depends upon more than that, specifically

Type of exercise (American or European)
Stock price
Strike price
Type of option (call or put)
Time remaining before option expires
Stock dividend, if any
Interest rates, and
Implied volatility

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In summary, going by the mathematical model, the same number of dollars investing in calls on a $6.48 stock will make as much as if they were invested in calls on a $449.54 stock when the stock goes up the same percentage, all else being equal. On a per contract basis, the more expensive stock would make the same percentage but more dollars. In the real worlds, it is essentially impossible to make that happen.

It all depends on what the option's parameters are.

Option pricing is most dependent on volatility. The higher a stock's volatility, the more expensive the option. Google is a more volatile stock than Sprint so its options will be more expensive.

That notwithstanding the price of GOOG. There are two components to an option price--the positive difference between the stock price and the option strike price and the time to expiration. Because GOOG jumped $90 or whatever, many out of the money calls became in the money and their value skyrocketed.

A friend of mine bought GOOG April calls with a 480 strike price the day before earnings. They cost $5. They were way out of the money but because of GOOG's volatility they were worth $5 even though they had one day till expiration.

With GOOG at 530, they suddenly became worth $50 for a gain of $45. A 900% return in one day---not bad!

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