FX Volatility Quotes: Smile Butterflies and Market Strangles
Summary
The document distinguishes smile butterfly quotes from market butterflies, also called broker flies, in foreign exchange volatility markets. It explains that at-the-money volatility, risk reversals, and butterfly quotes together describe key features of the volatility surface: its level, skew, and curvature. The answer also notes that conventions such as premium treatment and spot versus forward delta affect the conversion.
For a smile butterfly, the call and put volatilities can be recovered from the at-the-money volatility, butterfly, and risk reversal: add the butterfly to at-the-money volatility, then add or subtract half the risk reversal for the call or put. These values correspond to the delta used for the quotes. Market butterflies require a more involved calculation; the response does not give that conversion or a mathematical relationship between the two conventions. It briefly mentions a listed-market margin example, but does not establish that it applies to the question’s FX context.
Key ideas
- At-the-money volatility, risk reversals, and butterfly quotes summarize the level, skew, and curvature of an FX volatility surface.
- A smile butterfly and risk reversal determine the quoted call and put volatilities relative to at-the-money volatility.
- Market butterflies, also called broker flies, require a more involved conversion than smile butterflies.
- Delta conventions and premium treatment can affect how FX volatility quotes are interpreted.
Tags
Full text
# Smile Strangle and Market Strangle # Smile Strangle and Market Strangle What is the difference between Smile Strangle margin and Market Strangle Margin in fx derivative market? Is it just variation in convention or is there any mathematical relationship between the two? ## Answer by AKdemy (score 2) https://quant.stackexchange.com/a/63560 Do you mean actual margins for listed products or clearing on say CME? I am not familiar enough with this but a quick research shows that the CME seems to simply use 3 calls with a +1:-2:+1 configuration. Strikes need to be equidistant in this definition; ``` strike2 – strike1 = strike3 – strike2 ``` Maybe I am wrong but I am assuming you simply mean smile butterflies and broker flys (also called market strangles). Generally, it's mainly a means of quoting FX vol. ATM Delta neutral Straddles (DNS), Risk Reversals (RR) and Butterfly (BF) quotes completely describe the entire surface. ATM the level, RR the skew and BF the kurtosis. There are some complications like premium included / excluded Delta, Delta style (spot vs forward), spread models used etc. One such complication involves how the BF is quoted. To get actual vols for calls and puts, one needs to transform these and solve for call / put vol. Smile BF is simple: ``` RR = Vol of an OTM Call Option (C) - Vol of an OTM Put Option (P) BF = ( C + P ) / 2 - Vol of ATM DNS ``` it's simple to show that ``` C = ATM + BF + RR/2 P = ATM + BF - RR/2 ``` where you get say a 25 Delta call if you use 25D RR and BF respectively. The above uses smile BF but brokers frequently quote market BF (short broker fly). These are a bit more involved but FX Volatility smile construction by Dimitri Reiswich and Uwe Wystup explains this in more detail (if this link does not work anymore, it can be searched easily).
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