# Writing OTM puts and calls with strike prices beyond reasonable

I have a flaw in my logic that I am hoping someone could help catch since I am certain it's flawed.

Suppose AAPL is trading at \$200 (it's \$179 but i want to round it off for simplicity) right now.

I decide to write a call option with a ridiculous strike price of \$400 next week. A strike price of \$400 means that AAPL would have to double, which is probabilistic-ally speaking close to impossible.

I also decide to write a put option with a ridiculous strike price of \$10 next week. A strike price of \$10 means that AAPL pretty much crashes as a company, which is also close to impossible.

In a week, it is pretty obvious that AAPL doesn't go to \$10 or \$400, but stays at around \$200. I would get around a premium of \$200 for the written call and a premium of \$190, which to me doesn't make sense because everybody would be doing something like that and it would imply arbitrage. Also, who exactly would pay me this premium?

I observe how for AAPL there's no strike prices in these unreasonable ranges: https://finance.yahoo.com/quote/aapl/options/

the maximum lowest strike price is 130.00 while the maximum highest is 210.00.

I am thinking that on one hand, it is obvious that nobody wants to be on the other side of a trade like that so such a trade wouldn't exist in the first place. Is my thinking correct?

• I think I found a flaw in my thinking in the sense that the premium for those written calls and puts paid to me wouldn't be the[ strike price - original price], but would be the market price valued through black-sholes, which would be pennies? Commented Mar 14, 2018 at 5:48
• The bid price on those extremely OTM strike prices is ZERO so selling the strangle would net you nothing. Commented Mar 14, 2018 at 13:15

If Apple is trading at \$200 and you sell a Call with a strike price of \$400, the contract would be way out of the money and worth maybe a penny per share. The person is buying the right to buy 100 shares of Apple for \$400 per share which is of no value when the share price is \$200.

Same is true to sell the way out of the money Put. The person is buying the right to sell Apple shares for \$10, which no sane person would do if the market is trading at \$200 per share so the contract would maybe be worth a penny per share; IF you could find a buyer.

Now if you wrote a Call at \$10 and a Put at \$400 that would be a different story, but there is still risk to you if you're uncovered. Additionally, there's no real point to going so far out of the money because the price you at which you sell the contract will have the delta between the strike price and the market price built in on a 1:1 basis.

Say you wanted to make a market like this and want \$20 per contract for your trouble. So you sell a put option to someone with a strike price of \$400 for \$0.20 per share, you get your \$20. The holder of that contract buys 100 shares of Apple on the open market for \$20,000 and comes to you to sell the 100 shares for \$40,000. Oopse, that person just made \$19,980 at your expense. So what do you do to avoid this horrible situation? You include the "in the money" delta in the price of the contract when you sell it. Now your option is priced at \$200.20 for the \$400 strike Put option. Your holder paid you \$20,020, they can go buy 100 shares for \$20,000 and sell them to you for \$40,000, they'd lose \$20 in the deal so there's no point. If you sold at a strike price of \$500, you'd just sell the contract for \$300.20 and so on.

• Thank you, this is kind of what I was thinking. So basically the premium that a person gets paid when one writes a call or a put is determined by the market somewhere in the vicinity of the Black Scholes value. Commented Mar 14, 2018 at 6:28
• @user68991, The big flaw in your thinking above is the difference between "in" and "out" of the money, not what pricing model is used to determine the risk premium. If Apple is trading for \$200 per share, a \$10 strike Put is way out of the money and largely worthless because no one would want sell 100 Apple shares to you for \$10 per share when they could sell to the market for \$200 per share, but a \$10 Call is way in the money and worth \$190 per share, because the buyer could buy Apple shares from you for \$10 per share and immediately sell them to the market for \$200 per share.
– quid
Commented Mar 14, 2018 at 6:40
• With the stock at \$200, writing a \$10 call and a \$400 is a short guts strangle. While it's true that the position is uncovered, there's zero risk b/t \$10 and \$400 at expiration. Prior to expiration, the break even points would be narrower. Assuming fair pricing, this guts spread would offer the same return as writing the \$10put/\$400 call strangle. Commented Mar 14, 2018 at 13:30