FX options: volatility, skew and the price of protection

A premium contains more than direction

An FX option gives a contractual right connected to exchanging currencies or to a specified underlying derivative, depending on the product. Its value depends on the exchange rate, strike, time, interest rates, volatility assumptions and contract terms. A buyer can be directionally correct and still lose money if the move is too small or arrives too late relative to the premium.

The option must be described with currency units and the underlying clearly identified. A euro call against dollars is also protection against a particular dollar outcome, but platform labels may use different conventions. Options on futures are not identical to deliverable spot options. Exercise style, settlement and contract size belong in the analysis before any sensitivity calculation.

For a simple European euro call against dollars, the expiry payoff per euro is the greater of S − K and zero, where S and K are dollars per euro. With a strike of 1.10 and a premium of $0.02 per euro, an expiry spot of 1.115 produces $0.015 of payoff but a $0.005 loss per euro after the premium, ignoring its financing and other costs. Being in the money describes exercise value; it does not mean the buyer has broken even.

Implied volatility is a model input inferred from price

Implied volatility is the volatility value that reconciles an observed option price with a chosen pricing model and its other inputs. It summarizes pricing under that framework; it is not a direct observation of future realized volatility. Risk compensation, hedging demand, liquidity and model limitations can all contribute to differences between implied and subsequently realized volatility.

Comparisons should use matching maturities and conventions. A one-week option spanning a policy announcement can be more expensive in volatility terms than a nearby period with no comparable event. That is not automatically a mispricing. A long-dated annualized number also should not be compared directly with a one-day percentage move without a stated scaling model.

A volatility surface has both a strike dimension and a maturity dimension. Comparing an at-the-money one-month quote with a far-out-of-the-money one-year quote mixes two changes at once. For event analysis, first compare equivalent strikes or deltas across maturities; for skew analysis, hold maturity and the quoting convention fixed. Annualizing volatility does not remove event concentration. A short window containing a major announcement can have a high annualized number even when its absolute expected move scale is smaller than a longer window's.

Skew describes unequal protection prices

Options at different strikes often imply different volatilities. A risk reversal compares specified call and put implied volatilities, commonly at matched delta conventions. It can describe which side of the distribution carries more expensive protection, but it is not a probability that the currency will move in that direction.

Sign and delta definitions are essential. Premium-adjusted and unadjusted deltas can imply different strikes, and switching the base currency changes interpretation. A report that says skew is positive without identifying the pair, maturity, call convention and delta is incomplete. Even with those details, expensive downside protection can reflect insurance demand rather than a profitable forecast of future spot movement.

If a stated convention defines a risk reversal as call volatility minus put volatility, a call quote of 10.5% and a put quote of 12.0% produce −1.5 volatility points. That is a difference in implied-volatility inputs, not a 1.5% cash premium and not a forecast that spot will fall 1.5%. Both options also have strikes and premiums. A surface can become more skewed while the overall level of volatility falls, so level and asymmetry should be tracked separately.

Separate sensitivities and path effects

Delta approximates the immediate price sensitivity to a small underlying move, holding other model inputs constant. Vega approximates sensitivity to implied volatility, while time decay describes the effect of time passing under model assumptions. These are local sensitivities, not complete profit forecasts for large simultaneous changes. Delta itself changes, and bid–ask costs matter when adjusting a hedge.

For a simulated option, write scenarios with both the exchange rate and implied volatility changing. An announcement can create a favorable spot move while removing uncertainty and reducing implied volatility. Depending on strike, maturity and premium, the volatility decline and passage of time can offset some or all of the directional benefit.

Gamma describes how delta changes as the underlying moves. For a small move, a rough option-value change can combine delta × price change, one-half gamma × price change squared, vega × volatility change and theta × elapsed time, with units matched to the provider's definitions. This is a local approximation, not a substitute for repricing a large move. It also explains why a delta hedge made this morning need not remain neutral after a substantial afternoon move.

Use ranges cautiously

A square-root-of-time volatility calculation can provide a rough reference under strong assumptions, but exchange rates can jump and returns need not be normally distributed. A one-standard-deviation figure is not a barrier or a loss limit. The assumptions become particularly fragile around scheduled events, stressed liquidity and regime changes.

A disciplined worksheet records the executable premium, total possible premium loss for a simple long option, exercise mechanics and scenarios beyond the illustrative range. Selling options creates a different risk profile and cannot be treated as merely collecting the buyer's premium without further analysis. The goal here is to understand prices of uncertainty, not to recommend a particular structure.

For a further exercise, hold the underlying exchange rate unchanged and compare a short-dated option before and after an anticipated announcement. Specify different assumed volatility changes rather than inserting a single inevitable decline. The exercise highlights that time and uncertainty can change an option position even without a directional currency move.

The familiar square-root-of-time rule assumes a particular variance scaling; it is especially weak when risk is concentrated on one announcement date. Nor is a 25-delta option simply an option with a literal 25% real-world probability of exercise. Delta is a price sensitivity under a model and a quoting convention. Turning market prices into probabilities requires additional assumptions about risk premia and distributions, which should remain visible rather than disappearing behind a precise-looking percentage.