An Historical Perspective On The EURUSD Volatility Surface

Includes: FXE, UDN, UUP
by: Kevin Mulhern

The volatility smile is one of those interesting phenomenon that no one in finance can fully explain. The Black Scholes formula for pricing a plain vanilla European option gives the value of the premium given inputs for spot price of the underlying security, strike price of the option, the market risk-free interest rate, the time until expiry of the option, and the implied volatility of the option. It is possible to take the market price for an option and the other four inputs and work backwards to determine what the market is implying in terms of future volatility in a security. Performing this same work-out for many different puts and calls of different strike prices for the same underlying produces a curve called the 'volatility smile'. According to Black-Scholes theory, the volatility smile should be entirely flat, meaning that implied volatility does not change for different derivatives on the same underlying. In practice, the market ignores that theory by showing a variety of different shapes in volatility smiles.

What does the volatility smile (and surface) tell us about a given security or foreign exchange pair? In order to simplify this message, a measure of volatility skew is used called the Risk Reversal. Risk Reversal is denoted with a subtext which gives the delta (in % change) from spot that it measures. A Risk Reversal for a 10% move from spot would be denoted RR10. Risk Reversal subtracts the implied volatility of the Put option with a strike representing a 10% loss, from the implied volatility of the Call option with a strike representing a 10% gain. Since implied volatility is a proxy for option price (higher implied vol = more possibility of option expiring in-the-money), a positive risk reversal indicates that traders are buying more calls (at a given delta) than puts. If that is somewhat difficult to follow, understand that a higher Risk Reversal at a given date or option maturity implies that market participants are relatively more bullish (obviously, a relative simplification).

If we think in terms of smile graphs, an FX volatility smile that slopes downward implies that the market expects greater strengthening in the quote currency (because they are buying more puts than calls and a downward move implies a strengthening of the currency in the numerator). For example, observe the current vol smile for the EURUSD cross.

As you can see, traders are betting that the dollar strengthens against the euro because puts are carrying higher implied vols than the calls. Bloomberg adds in different expiry maturities, giving you some sense of the overall volatility surface of the EURUSD options market. Here is a table showing the current Risk Reversal measures on the EURUSD.

As time goes on, the skew as measured by the 25 delta RR and 10 delta RR is increasingly negative. This implies that market participants are skewing their purchases more towards puts as maturities increase. It may also be interesting to note that the term structure shows that the implied volatility starts to drop off beyond the 18 month maturity, indicating that most of downward volatility expected for the euro should occur within the next 18 months. Below is the entire volatility surface; it's important to keep in mind that the x- and y-axes are scaled linearly but jump around based on the inputs. I changed the viewing angle a bit to make it easier to discuss. What is interesting is that the surface slopes upward rapidly as you move farther negative in terms of puts. Additionally, as you move to the left (increasing maturity), you see implied volatilities increase, but then drop down after one year.

We can examine the EURUSD volatility surface at other dates over the past few years to observe how expectations have changed. Below is the volatility smile from March 2010, before the game-changing discovery of Greece's debt accounting trickery. Pay careful attention to the y-axis scale when comparing it to the 2012 smile.

It appears that traders were slightly less bearish on the euro two years ago, yet they quite obviously remained fairly negative in general on the currency. Compare the 2010 and 2012 smiles with the smile that was present in early 2008, before the full onset of the financial crisis. Again, pay attention to the y-axis shifts.

It's obvious that the 2008 smile had a substantially less bearish view of the euro. Though deep out-of-the-money puts were still showing a higher implied vol than deep out-of-the-money calls, the differential was significantly less apparent than in the later smiles. If we look even farther back to 2006, when there wasn't a hint of the impending housing bubble collapse, the EURUSD vol smile shows bullishness on the part of traders in the euro.

Our thesis is that a successful negotiation of the Greek default and bailout, with the limited market reaction, signals a turning point that presages a return to normality over the next few years. Though we won't argue the full fundamentals of that case here, we are suggesting that you sell EURUSD puts and buy calls if you agree (tending towards longer maturities). The idea is that the premium for implied vol you will receive by selling puts is inflated relative to the premium you would pay for calls. We like this trade because we aren't necessarily bullish on the euro, but believe that the fairly significant negative skew in the volatility surface will shift back towards its previous balance as bearish sentiment on the euro begins to erode.

Disclosure: I have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.