Disregarding why one might want to put on a synthetic long instead of just buying the underlying, does such a position tend to behave like the equivalent long stock over the life of the position? Are there pitfalls to be aware of? Assume this is on an index or some other underlying that pays no dividend, if it matters. A "what if" might be what happens if the S&P 500 shoots up (or tanks) after I have simultaneously purchased an ATM call and sold an ATM put on SPX. Will my profit (or loss) tend to track the S&P "exactly"? When the position is ATM, my P/L calculation shows delta ~ 100 with almost no gamma, vega, or theta. If I take that pricing and simulate the same trade after some 5% drop (i.e., I look at a synthetic long with a long 5% OTM call and a short 5% ITM put), I see a delta that has dropped to ~ 95 but the other Greeks are still pretty much hedged. The "current value" as shown in my P/L calculation is about right (down some $10K, which makes sense given that the position was initiated as a synthetic 100 shares on SPX and the index is down ~ $100). Am I missing something?
As long as put call parity hold, you should be OK. The only problem is making sure that your margin is fine so you are not forced out of your short put (aka, auto liquidation from some broker).
A synthetic stock position should exactly track the stock. There are some things that will effect the spread, such as changes in interest rates, changes in dividends, and if the stock is hard to borrow. In some instances you are better off being long the synthetic as opposed to long the stock, such as if the stock is hard to borrow. Here you will capture the hard to borrow rate with the synthetic as opposed to letting your broker make the money if you are only long the stock. If you are in a combo (synthetic) in the SPX it will exactly track the SP 500 future of that month. So If you are long the combo and short the future, you can leave them all on until expiration and they will all expire to cash. Remember that the combo tracks the future not the underlying SPX cash. The cash will stop at 3:00pm ct. while the future will trade until 315 with the options. Your margin will most likely be lower just trading the SP 500 future than trading the SPX combo, and there will be less slippage entering and exiting the position.
Great response, thank you very much. Outside of the 0:15 expiry difference, is there any other reason that DITM SPX LEAP calls "trade" at a discount to fair value; i.e., the ask can be well lower than the difference between the S&P 500 and the strike of the LEAP. My expectation is that one might not even get a fill at the ask, but there must be more to it -- no dividend, European option expiry, ???
All is due to put call parity. In European options put call parity *must*always hold which in some cases means that deep in the money calls can be traded for lower than intrinsic value. Remember that because there is no early exercise in European options, there is no arbitrage opportunity there. Most of the time those lower than intrinsic bids are due to just the option being too iliquid.
It's not just the bid. As an example, the ask on the Dec18 SPX 100 call is $1,850.80 (SPX = 2058.69), which implies the call is priced at ~ 95% of intrinsic value. I have no idea if it is actually available for purchase. At some point, the discount has to fade -- I admit I haven't really thought through all the implications.
Think if you put on this trade, bought the Dec 18 100 calls and sold the puts for .10 (puts really don't matter here) and then sold all the spx 500 stocks at the perfect ratio so you are short the index. You will pay interest on your long calls. You will pay dividends on all your short stock, for two and a half years. At one time a while ago, you would have gotten a good short stock rebate on your short stock, but no more. Hence the discount, as newwurldmn said.