Actually, there is another, little-known relationship called put/call symmetry that has to do with fair value of puts vs calls: Call(K) = Put(f^2/K) * (K/f)
==================== Pabst; Another strange but not real frequent pattern; especially on a day order, which sits there all day, occasional fills below bid price, buy to open long calls/long puts.[ISE,CBOE, BOX] Maybe MM's trying to help you cause of the times they chose not even to split bid ask spread.
and I thought I knew options trading... seems that these discussions are useful at the level that one trades, usually a stock trader adds greater returns to his portfolio through synthetic call/put positions in the options markets instead of the dynamic hedging that has been described in the previous comments. usually it takes a mathmatics or applied option theory class (or readings of a few sited text books) to incorporate those discussed concepts in one's trading mix.... usually one is doing the so called, up-stairs firm global risk hedging in using those calculations and they are never trusted to being done by hand, so that once programmed are relied upon time and time again and simply show up as a calculated number in a text column and one is told to keep that specific number within a tight range, else it probably will start setting off trading alarms on the head and supervisor's trading station.... usually knowing whether one has flat delta's or hedging against upside/downside gamma or additional theta is relevant to larger portfolios and not the average $1mm or less trader so, its all relative to your portfolio committed to the trade and what is being protected and especially whether this is your primary trading vechile / function or your secondary. clearly you can see that option trading can take on and replace the other primary stock and/or futures aspects of trading and become its own universe to trade in its own rights. clarify where you sit at the table first, then we can more correctly approximate who might be sitting on the other sides of the trade. cheers
Had a quick look at that, can't make it work. Any chance you could work an example ? I thought deriving a Call value from a Put value was simply... Call = Put - K + F. Riskarb I think the terminology may have confused. When I think in terms of fair value / ThVal it is the option value derived from IV/FV, rather than the Put / Call symmetry you were (apparently) talking about. Will do, but can you explain this first ? Thanks
Dude, I'm talking about put/call SYMMETRY, not put/call PARITY. This one is a model-dependent relationship assuming geometric (proportional) brownian motion. The forward here can be interpreted as a geometric mirror reflecting a call into a certain number of puts. Here is an example: Forward is at 5 Strike is at 6 Volatility is at 20% Time is 1 year First we calculate second strike (f^2)/K = 4.1167. Then we price a call with the original strike vs a put with a "reflection" strike: Call: .10736 Put: 0.08947 Now, we multiply value of the put by K/F = 6/5 = 1.2. This yields to us 0.10736. The symmetry holds. While this would not nessesarily hold given a skew/smile, this method is a good way of figuring out historical relationships between puts/call, i.e. if you are planning to do some smile or skew trades.
It's artifact of the distro & forward price, and is model-dependent. I am referring to p/c symmetry. Pricing of calls/puts. SLE has graciously shown the maths. I have some PDFs I can reference as well.
Appreciate the reply SLE. But I don't quite follow what, or should I say why you're testing P/C symmetry and assuming a flat vol surface because... using that assumption - they will always be symmetrical ??? This is the post I and others find confusing. I'll not ask you to explain it again, but thanks anyway for your time thus far.
No, the vol surface does not have to be flat, it has to have the same vol at reflection stirke. A truly-symmetrical smile (no skew) would keep put/call symmetry. The point of this is as follows - let's say you want to trade a risk reversal with call at X delta. Let's take the same example - stock at 5, call at 6 has X delta. Imagine that put of the same delta would be struk at 4.0, but symmetric strike is 4.17. Would you rather sell a call and buy a put or the opposite? ps. being long delta felt good yesterday and still feels good today.