Delta: Your Currency Exposure
Delta measures how much an option’s value changes when the underlying currency moves. In currency options, delta represents your net currency position, but you are always dealing with two currencies simultaneously.
A EUR/USD call option with a delta of 0.60 means you are effectively long 60 percent of the notional amount in euros and short 60 percent in dollars. If you own a 10 million euro call with 0.60 delta, it behaves like being long 6 million euros spot.
Crucially, every currency option is simultaneously two options: a EUR/USD call is both a euro call and a dollar put. When you buy the right to purchase euros at a fixed price, you are inherently selling dollars. This dual nature means currency options respond to economic events in both regions, interest rate changes in both currencies, and the relative strength between the pair.
Delta ranges from 0 to 1.0 for calls and 0 to negative 1.0 for puts. At-the-money options typically have deltas near 0.50 (or negative 0.50 for puts), while deep in-the-money options approach 1.0 and out-of-the-money options decay toward zero.
The key distinction in currency options: delta changes based on both spot movement and volatility shifts. Through triangular arbitrage relationships, every currency option implicitly affects other pairs. Long EUR/USD calls combined with long USD/JPY calls equals synthetic long EUR/JPY exposure.
Gamma: The Acceleration of Delta
Gamma measures how fast delta changes as spot moves. It tells you whether your directional exposure is stable or rapidly shifting.
High gamma means your position’s delta changes quickly. If EUR/USD rises 10 pips and your position has gamma of 0.05, your delta increases by 0.05. This acceleration creates both opportunity and risk.
Gamma peaks for at-the-money options and intensifies dramatically near expiration. The 10 a.m. New York cut, where most currency options expire, creates extreme gamma effects. In the final hour before expiry, dealers hedging large positions can drive violent price swings as they buy and sell massive amounts to maintain delta neutrality.
Weekend gamma presents unique challenges. Friday’s closing position must survive 60 or more hours of potential news flow. Many professionals avoid holding gamma over weekends, especially around elections or central bank meetings.
Vega: Volatility Sensitivity
Vega measures how option values change when implied volatility moves. Despite using the Greek letter nu, markets universally call this “vega.”
A position with vega of $100,000 gains that amount for each 1 percent rise in implied volatility. During the March 2020 crisis, EUR/USD volatility spiked from 5 percent to 16 percent. Positions long vega multiplied in value while short vega positions faced devastating losses.
Currency vega behaves uniquely due to central bank dominance. When the ECB meets, euro volatility rises, but so does Swiss franc, sterling, and even crosses like EUR/NOK. This correlation makes hedging difficult. You cannot offset euro vega with yen vega when both spike together during risk-off events.
Vega peaks for at-the-money options and increases with time to expiration. A three-month option has roughly 1.7 times the vega of a one-month option, making longer-dated options more sensitive to volatility changes.
Theta: Time Decay
Theta represents daily time decay: how much value an option loses each day, all else equal.
An option with theta of negative $25,000 loses that amount daily from time passage. Weekend theta is particularly painful. You pay three days of decay while markets are closed. At-the-money options suffer maximum theta, which accelerates exponentially near expiration.
The 10 a.m. New York cut concentrates global option expiries, creating intense theta effects. Options expiring at this cut often see extreme final-hour moves as dealers scramble to hedge massive exposures.
Rho: Interest Rate Sensitivity
Rho measures option sensitivity to interest rate changes, critical for currency options which involve two interest rates.
Currency options have two rhos: one for each currency’s rate. When the Fed hikes while the ECB holds steady, EUR/USD options reprice dramatically even without spot movement. The forward points shift, changing the option’s moneyness and theoretical value. This differential rho effect makes currency options uniquely sensitive to central bank policy divergence.
For longer-dated currency options, rho effects become substantial. A 50 basis point rate differential change on a one-year option can swing values by 2 to 3 percent, often exceeding the impact of theta or moderate spot moves. This sensitivity increases with time to expiration and differs by strike. In-the-money options are most sensitive to the currency they are denominated in.
Second-Order Greeks
Vanna
Vanna measures how delta changes with volatility (or equivalently, how vega changes with spot). During market stress, vanna creates unexpected directional exposure. Safe haven currencies (USD, JPY, CHF) typically have positive vanna. Their options gain protective delta as volatility rises. Risk currencies (AUD, NZD) show negative vanna, losing protective delta precisely when needed most.
Delta Decay
Delta decay measures how delta drifts with time passage. Also called overnight delta risk or time-based delta drift, this effect becomes most pronounced near expiration. For at-the-money options approaching expiry, delta decay accelerates dramatically. What appears to be balanced exposure at Friday’s close can shift significantly by Monday’s open, purely from the passage of time. The effect intensifies in the final 24 hours before the New York cut, where dealers managing large option books must anticipate how their positions will change while markets are closed.
Vega Convexity
Vega convexity measures how vega itself changes with volatility moves. This second-order effect matters most for volatility traders running large vega positions. Positive vega convexity means your position gains more vega as volatility rises, beneficial for long volatility strategies. Negative vega convexity means your vega exposure decreases as volatility rises, potentially leaving you under-hedged during market stress.
