Vol Surface

• In equity derivs, lower strikes tend to have higher implied vol because equities tend to rally slowly and fall hard. In FX it's more complicated, some vol smile are symmetric, some are highly skewed
• Vol smile tends to have higher implied vol on the "weaker" side of spot (direction in which spot is more likely to jump/be volatile). For example in USD/ZAR, vol smile is tilted so topside strikes has higher vol.

  
• When market making, if new information (trade/price) comes, vol surface must be updated.

  It can be done through:

  1. Changing the ATM
  2. Changing the wings of vol smile
  3. Changing the skew of vol smile

  
• Vanilla price requests that are quoted in vol terms are traded delta hedged. Black-Scholes formula is used to calc delta, and then a spot/forward hedge is transacted at the same time
• Vanilla price requests that are quoted in premium terms are traded live (no delta hedge)
• In G10 and some EM pairs, ATM contract is traded as a straddle
• In the other EM pairs, the ATM contract is traded as a single ATMF (at-the money forward) vanilla option with the strike equal to the forward, PLUS a forward hedge.
• When trading vanilla with strikes away from ATM, market convention is to always trade the OTM side. If the strike is above ATM, it will be traded as CCY1 call/CCY2 put. If the strike is below, CCY1 put/CCY2 call.

  This is important because:

  
• Two main approaches to generate core ATM curve:

  1. Input the ATM curve at the market tenors and interpolate to get ATM vol for expiry dates between the market tenors
  2. Use a model to generate the ATM curve and output thee ATM vol at the market tenors
• Linear Volatility interpolation often produces intuitively correct ATM curves but does not ensure positive forward variance

  
• Linear variance interpolation ensures positive forward variance but does not always create intuitive ATM curve

  
• Approximations that link ATM, 25d butterfly, and 25d risk reversals

  
• If butterfly and risk reversals contracts at all deltas are zero, the vol smile is flat, and any strike (for that tenor) will have the same implied vol
• In FX Vol Curve construction, ATM represents the central reference point, the butterfly lifts the wings symmetrically higher on both sides, and risk reversals tilt the smile one way or the other.

  
• Vega for a long ATM vanilla has a single peak at current spot. At higher vol the peak is still the same but the distribution is wider