# Sell deep in the money option

Hi Martinghoul, how have you been? Long time no see~~

I posted a thread about protective put strategy. There is something I really don't understand:

strike is K, and current stock price is S. Amercian put option is always worth more than the corresponding European put option (under same strike and maturity), since American put option is sometimes worth its intrinsic value K-S, it must hold true that the corresponding European put is sometimes worth less than its intrinsic value K-S, so does it mean that when the European put is worth less than the intrinsic K-S, I implement the protective put by buying the European put with premium p (less than its intrinsic K-S), then the worst case would be I only make profit of (K-S)-p?

just take a simple example: current stock price \$3, strike price for a European put is \$5, it seems possible for the European put to have premium less than (\$5-\$3)=\$2, say \$1.8 premium (because an American put can be worth its intrinsic \$2 and american put is worth more than the european put). so it is possible for the protective put strategy to always have positive profit, right? Minimum profit is \$5-\$3-\$1.8=\$0.2. I know this should be a mistake but I don't know where I am wrong??

many thanks, mate

It's not possible for an option to be worth less than its intrinsic value, whether American or European. In your example, the very minimum the (future value) of a \$5 put can be is \$2, if the market is trading at \$3 (i.e. your suggested price of \$1.80 cannot happen).

It's not possible for an option to be worth less than its intrinsic value, whether American or European. In your example, the very minimum the (future value) of a \$5 put can be is \$2, if the market is trading at \$3 (i.e. your suggested price of \$1.80 cannot happen).

Thank you very much mate.

American put option should be worth more than the european put, right? So when the american is worth is intrinsic value, the european put should be worth less than the intrinsic since it should be worth less than the american put, right?

Thank you very much mate.

American put option should be worth more than the european put, right? So when the american is worth is intrinsic value, the european put should be worth less than the intrinsic since it should be worth less than the american put, right?

That's the wrong way round. The minimum value of any option is the intrinsic, and we know the American is always worth the same or more than the European.

Thus if the American option is worth exactly the intrinsic, then the European must be as well, i.e. at that stage American = European.

(For example, if the market is \$15, then a \$1 call expiring tomorrow is worth \$14, whether American or European.)

That's the wrong way round. The minimum value of any option is the intrinsic, and we know the American is always worth the same or more than the European.

Thus if the American option is worth exactly the intrinsic, then the European must be as well, i.e. at that stage American = European.

(For example, if the market is \$15, then a \$1 call expiring tomorrow is worth \$14, whether American or European.)

when the american is worth exactly the intrinsic, at that stage the european should be worth less than that because it cannot be exercised immediately.

I thought american put and the corresponding european put only equal when they are exercised at maturity? So before option expires, american put has all the exercising opportunities that the european put would have if it could be exercised early as well. Hence logically, the two should not be equal before maturity?? When the amercian is only worth its intrinsic, at that right moment the european should have value less than the intrinsic?

Is this question essentially related to trading the liquidity factor of the pricing mechanism? If so, couldn't you just unravel the price and rip out a few knowns and see what you're left with? Also, does FX impact this at all what with it being US vs Eur?

when the american is worth exactly the intrinsic, at that stage the european should be worth less than that because it cannot be exercised immediately.

This statement is incorrect, you're attempting to apply flawed logic.

An option cannot be worth less than intrinsic, ever. Use this as your stating point (it immediately invalidates your statement).

This statement is incorrect, you're attempting to apply flawed logic.

An option cannot be worth less than intrinsic, ever. Use this as your stating point (it immediately invalidates your statement).

Well, apparently you are talking about american options not european options. I'm not making up that statement myself. I have read that from 'Options, Futures and Other Derivatives' by Hull. That's why I feel weird because obviously if that is true then you will have a 'always win' protective put strategy if you choose European put with less instrinsic value.

Well, apparently you are talking about american options not european options. I'm not making up that statement myself. I have read that from 'Options, Futures and Other Derivatives' by Hull. That's why I feel weird because obviously if that is true then you will have a 'always win' protective put strategy if you choose European put with less instrinsic value.

That's why it can't happen. If you can buy any option (whether American or European) for less than intrinsic, you can immediately lock in a risk free profit by hedging it with the underlying.

If you can do that, then it means the person on the other side is willingly giving you money - I'd suggest that is always going to be unlikely, irrespective of the mathematics.

Hull is an excellent book, try re-reading it.

That's why it can't happen. If you can buy any option (whether American or European) for less than intrinsic, you can immediately lock in a risk free profit by hedging it with the underlying.

If you can do that, then it means the person on the other side is willingly giving you money - I'd suggest that is always going to be unlikely, irrespective of the mathematics.

Hull is an excellent book, try re-reading it.

Thank you! What you said makes sense! But if European is worth only its intrinsic, you can still lock in a risk free profit, right?

Tell me how you would lock in a profit if you could buy the option at intrinsic?

Long dated, deep in-the-money European-style puts can certainly trade at a discount to instrinsic value partic in time of high interest rates.

As you can't exercise them early, their price is, effectively, the net present value of the intrinsic value.

This was the case on FTSE100 options in the early 90's (FTSE yield was around 4.5%, interest rates were circa 10%, so, net-net, for options with 200+ points of intrinsic and one year to go, the 6.5% discount on the forward value was more that the (very small), time value componant of the premium.

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S'kinda what I was trying to get at before. You have to unwind the price to see what's in the box before you make a decision otherwise you could be trading anything innit.

Tell me how you would lock in a profit if you could buy the option at intrinsic?

I bought the underlying at current price S; I bought put at premium p with strike K (K>S), p is its intrinsic value so p = K-S. At the option's maturity, if the underlying ends up at higher price than K, say S1, then I lock in a profit S1-S-p=S1-S-(K-S)=S1-K>0; if the underlying ends up at lower price than K, say S2 then I make S2-S+(K-S2)-p=0 profit. Therefore I can lock in profit S1-K or 0. Is that correct? thanks

Long dated, deep in-the-money European-style puts can certainly trade at a discount to instrinsic value partic in time of high interest rates.

As you can't exercise them early, their price is, effectively, the net present value of the intrinsic value.

This was the case on FTSE100 options in the early 90's (FTSE yield was around 4.5%, interest rates were circa 10%, so, net-net, for options with 200+ points of intrinsic and one year to go, the 6.5% discount on the forward value was more that the (very small), time value componant of the premium.

what you mean by that is if the strike is \$10, current underlying price is \$8, and it has 3 months left to maturity, then the present value (or the premium) of the option should be (10-8)/e^(3/12)r, r is risk free interest rate. So the present value is less than the intrinsic \$2?

Sell in-the-money option for profit if assigned.

Looking at just one option chain (IBM - expiring in 12 days - October monthly expiry) the original assertion that selling covered in-the-money options can be intrinsically profitable if you are assigned, appears to be true.

http://imageshack.us/a/img594/614/t2wditm20121007.jpg

You must click on the image to make it become full size.

Buy IBM at Ask (210.69) and then sell ITM 205 call at the same time (7.25), and then subsequently get assigned leads to a loss of 5.69 on the stock and 7.25 received from the option sell, so if assigned, you're up 1.56.

The problem with adopting this approach mechanically month in month out, is that the stock may fall by more than the 1.56 you hope to make.

So the worry is with capital loss on the stock side, if the stock declines. Although if IBM dropped to 204 on the day following this trade setup, and stayed below 205, then you get to keep the stock and the 7.25 option seller's premium because you're very unlikely to be assigned - but you have to be prepared to be assigned at any time, if you're an option seller.

But of course you'll be suffering an overall loss only when the stock drops below 210.69 - 7.25

Some covered call writers (sellers) also become irate if the stock rockets to say 250 and they get assigned and only receive 205.

Although if this stock price rise happened, if you were quick you could buy back the original option-sell at a loss, and sell another at strike 245 to emulate the original trade but at this higher level, if you haven't already been assigned.

There's an excellent pdf download for \$10 that will be around for a limited time, that explains this all in brilliant detail.

Just click "Add to cart" there. Don't worry about not having a PayPal account - PayPal will just take your credit card details.

The Rookies Guide to Options | Options for Rookies

There's good reviews for it on Amazon, but silly prices there for the print version, above \$100.

I think the point of the thread was that the OP thougt he'd found a risk-free lock-in. What you're doing is just getting long a range innit.

I bought the underlying at current price S; I bought put at premium p with strike K (K>S), p is its intrinsic value so p = K-S. At the option's maturity, if the underlying ends up at higher price than K, say S1, then I lock in a profit S1-S-p=S1-S-(K-S)=S1-K>0; if the underlying ends up at lower price than K, say S2 then I make S2-S+(K-S2)-p=0 profit. Therefore I can lock in profit S1-K or 0. Is that correct? thanks

Yes, this is correct. Put call parity tells you that C - P = outright position. Thus what you have described above is turning a deep ITM put into a very low delta call by hedging with the underlying.

Now the question you have to answer is --- who is going to sell you an option at intrinsic (ignore the effects of discounting).

The answer is no-one. And in the extremely unlikely event that someone DOES sell an option at intrinsic, it sort of means that there is ZERO chance of the market going back through the strike.

The very basis of option pricing is that there is no arbitrage, and you're trying to find it! Please read Hull again.

Yes, this is correct. Put call parity tells you that C - P = outright position. Thus what you have described above is turning a deep ITM put into a very low delta call by hedging with the underlying.

Now the question you have to answer is --- who is going to sell you an option at intrinsic (ignore the effects of discounting).

The answer is no-one. And in the extremely unlikely event that someone DOES sell an option at intrinsic, it sort of means that there is ZERO chance of the market going back through the strike.

The very basis of option pricing is that there is no arbitrage, and you're trying to find it! Please read Hull again.

thanks!
why it turns into a low delta call? Is that because the strike price K is higher than the current underlying price so the delta of the call is lower?? Why we don't want very low delta call?

What you're doing is just getting long a range innit.

Yes, that's an interesting way to look at it.

Reminds me of a bet on BetOnMarkets:

If IBM closes on October expiry day above 205.25 then you win 1.56
(as the stock will probably be assigned - but no guarantee, of course).

Cost of bet: 203.44

Otherwise you take whatever loss the stock is showing, below 203.44.

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