The conversion market pre-dates listed options. You can make a call(put) a put(call) with shares. An example. You're long the XYZ 50P. XYZ has dropped and you're now bullish. You have a choice--you can cover your profitable put and buy a call, or you can buy 100 shares which results in you holding a synthetic long 50C. One transaction (conversion to synthetic) rather than two (cover, buy call) and therefore less edge loss as you're not losing edge on the put sale and call purchase. The difference between a put and a call is the underlying. You can literally convert a put to a call and vice versa. Long 50P (existing position) + 100 shares = synthetic long 50C. The payoff is equivalent. The conversion market is the most basic spot/vol arbitrage. Long stock + put = synthetic call. Short stock + call = synthetic put. Google "option conversion market" and you'll get it.
You're confusing replication with conversion. This is an OOM easier to follow and there are no maths involved.
To elaborate; buying 100 shares (while holding the 50P) results in a synthetic 50C. 1. You gotta want to buy the 50C instead of another strike, but a., it's equivalent to the natural 50C in all ways and b., the stock purchase will involve less edge loss than covering the 50P and buying the natural 50C. Less comms. 2. One stock transaction (long 100 shares) vs. two options transactions (cover 50P; buy 50C). Simply buying the 100 shares converts your long 50P into a long 50C. The utility of synthetics in practice is to avoid deep ITM legs. Assignment risk (if short), more interest in OTM than deep ITM, less mkt impact on singles, arbitrage relationships, etc.
Go to whatever front end you use and plot the payoff of a long ATM call and then compare the payoff to that of the same strike long ATM put + long 100 shares.
This is freaking awesome! I honestly had no clue before reading thoroughly each of your replies to this post, thank you very much for the eye opening information.
You seem like the perfect candidate to help my with this head scratching, My first exposure to understanding the use of deep ITM options was when a friend showed me a trade where the goal is to be assigned on both legs for full profit (He is a new generation, 'Robin Hood gang' so he doesn't care about any commissions besides the bid/ask spread or assignment fees), he made a debit spread with deep ITM puts of Amazon, very far above the stock price at that moment, on a Thursday with clear momentum loss (neutral to bearish trade) of the trend, making this a high probability trade. He paid around $16 per contract, got assigned in both legs for a $4 profit, $20 width. Same case the other way around, with deep ITM calls being neutral to bullish, max profit if assigned both legs. I had an initial barrier to break, I couldn't get in my head messing with puts ABOVE the current underlying price, or calls BELOW. Does that strategy is common or has an specific name? After I spent some time studying it, taking the amazon example, wouldn't it be exactly the same to replicate that trade with deep OTM Calls, shorting the spread to collect the $4 instead of being long, maximum risk $16. And keeping the credit with the goal of not being assigned any leg? (it seems like a more common sense approach, avoiding assignment). It took me a while to trying to understand this TBH but reading your replies to this post I guess this is easy cake, completely easy to analyze for you. And I think I am missing something, maybe the risk/reward doesn't make this a good approach in the long run, even with the high POP.
He's in a vertical. Short put at 3480, long put at 3500. You cannot compare an equidistant (from share price) DITM call vertical against a DITM put vertical. There is no arbitrage to prevent those equidistant ("cash" moneyness) spreads to trade at equal volatilities. We refer to this difference in vol-lines as the "risk reversal" vol. He paid a debit < strike width, in this case, $16 for a 20 point wide vertical spread. He could have shorted the 3480/3500C vertical (short 3480C; long 3500C) for a $4.00 credit. Same payoff as the DITM bear put spread. He cannot be assigned on both. He owns the 3500P. So if he's assigned on the 3480 put he is long shares from 3480 and remains long the put. It doesn't matter where the stock is. The resulting position is a long synthetic 3500 CALL. He's still long a put and long stock, but the only risk is that of a deep, deep OTM long call. The result is essentially zero risk with the "lost" premium as represented by the premium on the (natural) actual 3500 call. IOW, the 3500 call mkt represents the cost of holding that DITM long put. TL; DR? Don't trade DITM. Trade the synthetic. Shares at 3400. The dude is looking to buy the (bear) 3480/3500 put vert. He should roll over until the urge passes as fill quality is marginally improved in shorting the 3480/3500 call vert. The put and call vertical pricing is governed by the box arbitrage.
You wouldn't, but a synthetic long call would be short a put at 20-strike, long a call at 20-strike, long a put at 19-strike. You'd be long the synthetic 19C.
Thank you very much for your valuable insight, as I can see I wasn't that wrong to see some kind of relation with the synthetics you were explaining and my doubt. Sorry that I confused the wording, you are absolutely right I meant that he was assigned the short put an exercised the long one as he made that trade on a Thursday with the options expiring on friday, he didn't have the cash or the margin to be assigned because he opened 10 contracts so his RH account showed the +3.5MM minus the -3.48MM. 'He could have shorted the 3480/3500C vertical (short 3480C; long 3500C) for a $4.00 credit. Same payoff as the DITM bear put spread.' Thanks for confirming, That's what I was thinking and i'm glad I got the reasoning right, maybe the puts would have better liquidity but it seems like a more common sense approach. I will surely re-read all you replies on this thread and will begin to research on the synthetics to completely grasp the concept and application.