Relation between ATM, RR and BF

In FX derivative market, why does vol spread of ATM > RR > BF? ATM is the most liquid and intuitively it should have the lowest spread. Please help me in understanding the rational behind the above logic.

The ATM is an outright position (long 50 delta put and 50 delta call) so the main exposure is vega. It is the riskiest of the three, and demands a higher bid-offer spread from market makers to compensate them for the additional risk.

The RR is a spread position (long 25 delta call, short 25 delta put) with zero vega, the main exposure is skew. Because the outright risk is hedged, market makers are willing to quote a tighter bid-offer spread.

The BF is a spread of spreads (long 25 delta call vs short 50 delta call, and long 25 delta put vs short 50 delta put) so it has no exposure to vega or skew. The main exposure is curvature. Hence it carries even lower risk than the ATM and RR, so market makers are willing to quote the lowest bid-offer spread.

• Thank you so much Chris. The explanation is really very helful. I am very new to the field. Is it safe to infer from your answer that Vega exposure is more riskier than skew which in turn is more riskier than curvature? Can you please help me understand why is it so? Thank you so much for taking your time out.
– Ussu
Oct 6 '19 at 7:54
• That’s one way of seeing it. Another way is - the 25 delta put and call are positively correlated instruments (once their delta is hedged). If you are long one and short the other (a risk reversal) you have hedged the main directional exposure (vega) so your risk is reduced. Similarly the 25/50 delta call spread and the 25/50 delta put spread are positively correlated, and if you are long one and short the other (which is a butterfly) you have hedged the main exposure (skew, since the vega is already hedged in each spread) and your risk is again reduced. Oct 6 '19 at 20:08
• Thank you so much. These explanations are really helpful. Few follow up queries: 1. You assumed the trades are delta neutral so 25D call and 25D put are correlated as per put call parity. Is it fair to assume they are delta neutral? 2. 25/50 delta call and 25/50 delta call are positively correlated. Why do you say this? Any mathematical/ intuitive way of understanding this?
– Ussu
Oct 6 '19 at 20:39
• 1. Yes, most option analysis assumes you have hedged the delta already by trading in the underlying. The delta exposure is the least interesting part of an option because it is so easy to hedge 2. I said the call spread and the put spread are positively correlated, simplest way to understand it is that they are both exposed to skew (ie if the volatility smile becomes steeper or flatter, the value of the call spread and the put spread change in the same way, ie both increase or both decrease). Oct 6 '19 at 21:25
• Hi Chris, I can't thank you more for clarifying doubts which I had for a long time and I could not get answers even after trying so much. It seems you have really good knowledge about this. Thank you so much.
– Ussu
Oct 8 '19 at 9:45